More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
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Our breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
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“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
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Additionally, each book published by IntechOpen contains original content and research findings.
\\n\\n
We are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\n
Simba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\n
IntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\n
Since the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\n
Our breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n
“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\n
Additionally, each book published by IntechOpen contains original content and research findings.
\n\n
We are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n
\n\n
\n'}],latestNews:[{slug:"intechopen-supports-asapbio-s-new-initiative-publish-your-reviews-20220729",title:"IntechOpen Supports ASAPbio’s New Initiative Publish Your Reviews"},{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"}]},book:{item:{type:"book",id:"136",leadTitle:null,fullTitle:"Smart Wireless Sensor Networks",title:"Smart Wireless Sensor Networks",subtitle:null,reviewType:"peer-reviewed",abstract:"The recent development of communication and sensor technology results in the growth of a new attractive and challenging area - wireless sensor networks (WSNs). A wireless sensor network which consists of a large number of sensor nodes is deployed in environmental fields to serve various applications. Facilitated with the ability of wireless communication and intelligent computation, these nodes become smart sensors which do not only perceive ambient physical parameters but also be able to process information, cooperate with each other and self-organize into the network. These new features assist the sensor nodes as well as the network to operate more efficiently in terms of both data acquisition and energy consumption.\nSpecial purposes of the applications require design and operation of WSNs different from conventional networks such as the internet. The network design must take into account of the objectives of specific applications. The nature of deployed environment must be considered. The limited of sensor nodes� resources such as memory, computational ability, communication bandwidth and energy source are the challenges in network design. A smart wireless sensor network must be able to deal with these constraints as well as to guarantee the connectivity, coverage, reliability and security of network's operation for a maximized lifetime.\nThis book discusses various aspects of designing such smart wireless sensor networks. 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The company empowers customers with sensor-end to application-end platform solutions to discover opportunities and capture value from actionable insights as well as co-create with domain experts using advanced artificial intelligence (AI)/machine learning (ML) tools. Dr. Tan is concurrently the associate editor of the IEEE Sensors Journal and the industrial chair of IEEE Singapore section. 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\n\t\t\t
1. Introduction
\n\t\t\t
Nowadays, the demand and the necessity for the use of materials with specificcharacteristics have increased in many engineering fields. Due to this necessity of making new materials, composite materials have been an alternative, or maybe the unique option, to attempt a large number of design requirements suchas high strength-to-weight ratio,high resistance to mechanical shocks, chemical attacks, corrosion, and fatigue, that cannot be obtained only from the commonly used structural materials (metals, ceramics, polymers and wood). Because of this, their applications are present in the main industries such as aerospace, automotive, marine, and sportive
\n\t\t\t
Thanks to their flexibility characteristicsthere are many combinations and arrangements and, consequently, constitutive properties, that are possible to be achieved. This particularity represents one of the main advantages of these materials. Nevertheless, some factors related to arrangements as the number of layers and the orientation of the fibers can introduce abehavior called anisotropy that, in the most of the cases, is not required. The anisotropy makes the structural analysis more complex due to increasing the number of independent variables, as for example, the number of bending and extensional elastic stiffness constants.
\n\t\t\t
Recently, wide part of works presented by scientific literature whose goal is to identify constitutive parameters of materials (these being composites or not) is based in the called “inverse problems”. Experimental data such as geometry, resultant forces and strain (or stress) fields are used as input data, and the unknown variables are the required constitutive parameters. In general, the solution is basically associated to two methods: iterative (or also called indirect methods) and non-iterative (or also called of direct methods). The first one is related to optimization problems where the design variables are constitutive parameters and the objective function represents, in general, a residue (or error) between experimental and numerical (generally obtained by finite elements) data. For the numerical simulations, it is considered structures that have the same geometrical characteristics and boundary conditions of the real ones. For each step, required parameters are checked out, and, the optimum represents the iteration whose residue (objective function) has its lowest value. Unlike indirect methods, the direct methods are ones where the required parameters are computed from the solution of constitutive equation(s) that are functions of these parameters.
\n\t\t\t
In general, according to the type of experimental test, it is possible to separate the methods of elastic property identification in two categories: static (destructives and non-destructives) and dynamic methods (non-destructive), as shown in Fig.1. A large number of identification techniques that use data from these categories of tests have been proposed, especially ones dedicated to composite materials. It is possible to say that these techniques identify effective properties of the entire material. The way as each formulation is built, and, the adopted procedures and devices are the main differences among the many proposed methodologies.
\n\t\t\t
Static tests with monotonic load are experimental tests that were more commonly used in the last years, and maybe the simplestones, for this material property identification. Despite the simplicity of these tests, some aspects render them less attractive than dynamic tests, such as the fact of requiring a number of samples with fiber orientations according to standard norms, for example, American Society for Testing and Materials (ASTM), which, in the most of cases, are not in accordance to the real characteristics of the required material. Furthermore, some variables difficult of controlling during the tests can contribute to worsen the experimental results, e.g., the presence of non-uniform stress fields near the ends of the sample from the clamped boundary conditions. For these reasons, dynamic tests have been considered an interesting alternative. In general, they are tests that combine experimental data with numerical methods, and allow the identification of elastic constants from only one unique sample or even from composite material part. Sample is usually thin plate (that reflect Kirchhoff’s hypotheses), cylindrical shell, or beam. In many cases, input data of the numerical methods are natural frequencies and/or mode shapes.
\n\t\t\t
Figure 1.
Methodologies more used to identify elastic properties of materials.
The majority of works identifies only the bending stiffness matrix or directly the engineering elastic constants. However, the extensional elastic stiffness matrix is also needed to model composite materials under multi-axial loads. In general, these stiffness matrices are independent. The extensional stiffness matrix relates the in-plane resultant forces to the midplane strains, and, the bending stiffness matrix relates the resultant moments to the plate curvatures. In a laminate composite, if only the stacking sequence of layers is changed, the bending matrix is changed but the extensional matrix remains the same. In other words, different laminates can have different bending stiffness matrices and the same extensional stiffness matrix. It is not possible to obtain the extensional matrix from the bending matrix. It will be possible only if the stacking sequence of layers and their thickness are known and, also, if the material is the same for all lamina.
\n\t\t\t
Sometimes, it is more convenient to use effective laminate engineering constants rather than the laminate stiffness. These effective laminated engineering constants may be easily obtained from the extensional elastic constants. However, due to difficulties on experimental in-plane modal analysis, such as the necessity of using specific devices to measure in-plane displacements and to excite high frequencies, the identification of extensional elastic stiffness constants using modal testing is less attractive. The main challenge to perform in-plane vibration testing is the excitation and measurement ofonly in-plane and not out-of-plane vibration modes. Today there are some new techniques that are suitable for this kind of problems, for example, the excitation by piezoelectric (PZT) and measurements by digital image correlation.
\n\t\t\t
In this chapter, a review about the VFM applied to compute bending elastic stiffness constants proposed by Grédiac& Paris, 1996 is presented. Furthermore, a formulation based on the VFM is proposed in order to identify the extensional elastic stiffness matrix ofKirchhoff’s thin plates. The linear system of equations that provides the required elastic constants is obtained from differential equations that govern the forced vibration of anisotropic, symmetric and non-damped plates under in-plane loads. The common procedures to find the weak form (or integral form) of these equations are applied here. The correct choice of weighting functions (which are the virtual fields) and mode shapes representsa key characteristic to the accuracy of the results. Numerical simulations using anisotropic, orthotropic, quasi-isotropic plates are carried out to demonstratethe accuracy of the methodology.
\n\t\t
\n\t\t
\n\t\t\t
2. Identification of elastic constants using VFM
\n\t\t\t
\n\t\t\t\t
2.1. Review of the Virtual Fields Method - VFM
\n\t\t\t\t
The VFM has been developed for extracting constitutive parameters from full-field measurements and it is associated to problems of identification of parameters from constitutive equations. Two cases are clearly distinguished: constitutive equations depending linearly on the constitutive parameters and non-linear constitutive equations. The type of constitutive equations is chosen a priori for its relevancy and objective of it is to determine the parameters which govern the constitutive equations. The main difficulty comes from the fact that the measured displacement or strain components are generally not directly related to the unknown parameters (Grédiac et al., 2006), and no closed-form solution for the displacement, strain and stress fields is available.
\n\t\t\t\t
Mathematically, the VFM is based on the principle of virtual work and can be written as:
where V is volume of the solid, σ is the actual stress tensor, ε\n\t\t\t\t\t* is the virtual strain tensor, T is the distribution vector of loading tractions acting on the boundary, S\n\t\t\t\t\t\n\t\t\t\t\t\tf\n\t\t\t\t\t is the part of the solid boundary where the tractions are applied, u* is the virtual displacement vector, f is the distribution of volume forces acting on V, ρ is the density and γ the acceleration. Eq. (1) is verified for any kinematically admissible virtual field (u*,\n\t\t\t\t\tε\n\t\t\t\t\t*). Kinematically admissible means that u* must be continuous across the whole volume and it must be equal to the prescribed displacement on the boundary S\n\t\t\t\t\t\n\t\t\t\t\t\tf\n\t\t\t\t\t where displacements are prescribed. Let’s introduce the constitutive equations in the general case as:
whereg is a function of the actual strain. Thus, when constitutive equations are introduced and volume forces are disregarded, Eq. (1) can be rewritten as:
It is possible to see in Eq. (3) that each virtual field originates a new equation involving the constitutive parameters. The VFM relies on this important property. It is a method based on setting virtual fields that provide a set of equations. This set of equations is used to extract the required unknown constitutive parameters. The correct choice of the virtual fields that combine to actual fields in Eq. (3) is the key issue of the method. Their number and their type depend on the nature of g in Eq. (3).
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
2.2. Review of the identification method of bending elastic stiffness matrix
\n\t\t\t\t
The method proposed by Grédiac&Paris,1996, consists of obtaining elastic constants based on the partial differential equation that governs the transversal vibration of an anisotropic thin plate (Kirchhoff’s plate). This equation is given by:
where D\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\t are thin plate bending stiffness constants; ρis the mass density of the material; h is the plate thickness; x and y are coordinates of the plate; t is time; and w(x,y,t) is the deflection function that represents the transversal displacement of a point of the plate at an instant t. Eq. (4) doesn’t state the global equilibrium of the plate since the excitation force and damping are not considered. However, for many composite materials, as for example, aeronautic carbon epoxy tested in this work, the damping is low enough to disregard its contribution in the formulation. Besides, if the input data refer to resonant response of the plate, the work provided by the excitation is balanced by internal dissipation of the plate. A detailed discussion about when excitation and damping should be considered in Eq. (4) can be found in Giraudeau&Pierron, 2006.
\n\t\t\t\t
After some mathematical manipulations in Eq. (4), Grédiac& Paris,1996 obtained a linear system in which the unknown variables are the elastic constants. Briefly, the sequence of operations is as follows: (a) multiply both sides of Eq. (4) by an arbitrary weighting function; (b) integrate twice by parts along the plate domain; (c) eliminate the boundary integrals by applying the free-edge boundary conditions; (d) decompose the displacement function w(x, y, t) as a product of the deflection amplitude Φ and sin(ѡt), where w is the out-of-plane natural frequency of a particular mode shape of the plate; and (e) choose appropriate weighting functions and mode shapes to build the matrix of the linear system. At this point, as Grédiac& Paris, 1996 explain, the choice of mode shapes associated with the weighting function is extremely important for the accuracy of this method. Three particular modes are strongly dependent on the required coefficients D\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\t: a twisting mode that strongly depends on terms D\n\t\t\t\t\t66,D\n\t\t\t\t\t16, and D\n\t\t\t\t\t26; a bending mode along direction 1 that strongly depends on terms D\n\t\t\t\t\t11, D\n\t\t\t\t\t12, and D\n\t\t\t\t\t16, and a bending mode along direction 2 that strongly depends on D\n\t\t\t\t\t22, D\n\t\t\t\t\t12, and D\n\t\t\t\t\t26. These modes present smooth curvatures and are generally among the first modes, with lower frequencies. If these modes are not found, it is recommended to use modes that have similar shapes to them. Furthermore, they are modes that can be approximated by quadratic functions with constant curvatures: x\n\t\t\t\t\t2, y\n\t\t\t\t\t2, and xy. For this reason, these quadratic functions were the weighting functions chosen by Grédiac& Paris, 1996. Thus, using these previous quadratic-weighting functions, the following simplified system of equations can be obtained:
where, considering L as the number of modes used in the linear system of equations, K is a 3L x 6 matrix, D is a 6 x 1 matrix, and C is a 3L x 1 matrix. As can be seen, Eq. (7) is an overdetermined system of equations. The solution can be found by least squares:
2.3. Identification method of the extensional elastic stiffness matrix
\n\t\t\t\t
In the general case of composite laminates, each lamina is assumed to have orthotropic material properties. After the assembly, the behavior can be anisotropic due to the interaction of different laminas. Considering a plate under plane state of stress and using Hooke’s generalized law, stresses can be integrated over its thickness yielding the following force-deformation equations:
where N and M are vectors that contain normal forces and resultant moments, respectively, A is the extensional elastic stiffness matrix, B is the coupling elastic stiffness matrix (B is a null matrix in the case of a symmetric laminate), D is the bending elastic stiffness matrix, ε and κ are vectors that contain middle plane linear strains and rotations, respectively. Considering a symmetrical (B = [0]) and fully anisotropic laminate under free-edge in-plane vibration (the plate is not under bending) and using the equilibrium relations, the following equations can be written:
\n\t\t\t\t
\n\t\t\t\t\t\n\t\t\t\tE10
\n\t\t\t\t
\n\t\t\t\t\t\n\t\t\t\tE11
\n\t\t\t\t
where A\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\t are the elements of matrix A (i,j = 1,2,6); ρ is the mass density; h is the plate thickness; x and y are the coordinates in the plate plane; t is the time, and u(x,y,t) and v(x,y,t) are functions that represent the displacements along x and y direction, respectively, of a point with coordinates (x,y) of the plate at an instant t. Multiplying Eq. (10) by a weighting function W(x, y) and integrating along the domain of the plate, we can obtain:
\n\t\t\t\t
\n\t\t\t\t\t\n\t\t\t\tE12
\n\t\t\t\t
whereΩ is the plate domain. Using chain rule, i.e.,
where Γ is the boundary domain, and n\n\t\t\t\t\t\n\t\t\t\t\t\tx\n\t\t\t\t\t is the component of the normal unity vector in directions x, the left hand side terms of Eq. (12) can be written as:
\n\t\t\t\t
\n\t\t\t\t\t\n\t\t\t\tE15
\n\t\t\t\t
wheren\n\t\t\t\t\t\n\t\t\t\t\t\ty\n\t\t\t\t\t is the component of the normal unity vector in direction y. From the constitutive equation, one has:
whereN\n\t\t\t\t\t\n\t\t\t\t\t\tx\n\t\t\t\t\t and N\n\t\t\t\t\t\n\t\t\t\t\t\ty\n\t\t\t\t\t are axial forces per unit length along directions x and y, respectively, N\n\t\t\t\t\t\n\t\t\t\t\t\txy\n\t\t\t\t\t is the shear force per unit length along plane xy, ε\n\t\t\t\t\t\n\t\t\t\t\t\tx\n\t\t\t\t\t and ε\n\t\t\t\t\t\n\t\t\t\t\t\ty\n\t\t\t\t\t are the middle surface axial strain along directions x and y, respectively, and γ\n\t\t\t\t\t\n\t\t\t\t\t\txy\n\t\t\t\t\t is the shear angular strain along plane xy. Rewriting Eq. (16), one obtains:
Multiplying Eq. (17) by a weighting function W and by n\n\t\t\t\t\t\n\t\t\t\t\t\tx\n\t\t\t\t\t, which is the x component of unit normal vector n, and integrating on the boundary Γ, one obtains:
Multiplying Eq. (19) by a weighting function W and by n\n\t\t\t\t\t\n\t\t\t\t\t\ty\n\t\t\t\t\t, which is the y component of the unit normal vector n, and integrating on the boundary Γ, yields:
Now, if free-edge boundary conditions are considered, boundary integrals of Eq. (22) vanish. Considering that the plate is vibrating, functions u and v can be written as:
where\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tϖ\n\t\t\t\t\t\t\n\t\t\t\t\t is the in-plane natural frequency associated to any in-plane mode, and U(x,y) and V(x,y) are the displacement amplitudes along directions x and y, respectively, of a point with coordinate (x,y). In this sense, the amplitude is only a function of coordinates x and y. Eliminating the boundary integrals of Eq. (22), substituting Eqs. (23) and (24) into Eq. (22), and considering any mode j, one obtains:
\n\t\t\t\t\t\tEqs. (25) and (26) are theoretically valid for isotropic, orthotropic, or anisotropic plates, provided that the laminate is symmetrical. As it can be seen, the function W is arbitrary since itself and its first order derivative is continuous in the domain Ω. Amplitudes U(x,y) and V(x,y), and frequencies \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tϖ\n\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t are obtained from dynamic tests. Dimensions of the plate and parameters ρ and h can also be easily measured on the sample plate. Thus, the next steps are the choice of a suitable numerical method to compute the derivatives and integrals in Eqs. (25) and (26). Furthermore, suitable mode shapes and weighting functions should be chosen. In this work, finite differences and Gauss-Legendre numerical integration scheme are used to compute these derivatives and integrals, respectively. For numerical reasons, modes with several sign changes in the mode shape are avoided because their numerical derivatives and integrals are more sensitive to errors (Grédiac& Paris, 1996). Generally, first modes present more smooth curvatures and are, at the same time, easier to be obtained experimentally. It is worth noting that in-plane modal analysis presents much higher frequencies than transverse modal analysis (bending modes). This is because stiffness along direction x and y is much higher than stiffness along the transversal direction of the plate. For numerical reasons, smooth mode shapes associated with smooth weighting functions are preferred. For all these reasons, and in order to simplify Eqs. (25) and (26), the following group of weighting functions are proposed:
\n\t\t\t\t\t
W(x, y) = x2, which applied to Eqs. (25) and (26) provides the following integral equations:
where, considering L modes, K is a 6L x 6 matrix in Eq. (40), A is a 6 x 1 matrix, and C is a 6L x 1 matrix in Eq. (40). Eq. (40) is an over determined system. Thus, the solution can be found by least squares:
from where the extensional elastic constants A\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tij\n\t\t\t\t\t\t are computed.
\n\t\t\t\t
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
3. Results and comments
\n\t\t\t
A commercial finite element code (ANSYS 11.0) was used to give particular mode shapes and their corresponding natural frequencies from both in-plane and out-of-plane numerical modal analysis. Element SHELL99 was used and plates under free-edge boundary conditions were considered.
\n\t\t\t
To exemplify the method proposed by Grédiac and Paris (1996), it was used an anisotropic plate with dimensions 0.450 x 0.350 x 0.0021 m and density 1500 kg/m3. It was used a laminate with 8 plies, [0 45 90 135]S, and the following engineering elastic constants by ply: E\n\t\t\t\t1=120 GPa (Young’s module along the principal direction 1), E\n\t\t\t\t2=10 GPa (Young’s module along the principal direction 2), G\n\t\t\t\t12=4.9 GPa (shear module along the plane 1-2), and ν\n\t\t\t\t12=0.3 (Poisson’s ratio along the plane 1-2). A mesh of 651 nodes was used. Fig. 2 shows the three modes used to identify the required properties. As can be seen, depending on type of material anisotropy, it is not possible to find all three modes necessary to apply the method. In this case, it is necessary to find the more approximated ones.
\n\t\t\t\tTable 1 shows the bending elastic stiffness constants computed using the engineering constants and the classical theory of laminates, and it also shows the errors computed after applying the identification method. As can be observed, the technique is able to find very satisfactory results when it is used the correct modes. The problem of this technique is the high sensitivity to noise presence because of second-order derivatives. More results and comments about this method can be found in Grédiac& Paris, 1996.
\n\t\t\t
In order to verify the accuracy of the extensional elastic stiffness identification method, it was used six graphite/polymer symmetric laminated plates (Table 2): a fully anisotropic with all A\n\t\t\t\t\n\t\t\t\t\tij\n\t\t\t\t different from zero (i,j = 1, 2, and 6); a cross-ply orthotropic with A\n\t\t\t\t11 = A\n\t\t\t\t22, A\n\t\t\t\t16 = A\n\t\t\t\t26 = 0, and A\n\t\t\t\t11 – A\n\t\t\t\t12 ≠ 2A\n\t\t\t\t66; a 0° unidirectional orthotropic; a 30° unidirectional orthotropic (generallyorthotropic); a +30°/-30 angle-ply orthotropic; and a quasi-isotropic with A\n\t\t\t\t11 = A\n\t\t\t\t22, A\n\t\t\t\t16 = A\n\t\t\t\t26 = 0, and A\n\t\t\t\t11 – A\n\t\t\t\t12 = 2A\n\t\t\t\t66. These laminates have 8 plies with the following engineering elastic constants by ply: E\n\t\t\t\t1=155 GPa, E\n\t\t\t\t\n\t\t\t\t\t2\n\t\t\t\t=12.10 GPa, G\n\t\t\t\t12=4.4 GPa, and ν\n\t\t\t\t12=0.248. Dimensions considered were 0.450 x 0.350 x 0.003 m (x, y, and z plate coordinate axis, respectively), for the rectangular plate, 0.350 x 0.350 x 0.003 m, for the square plate, and, the density material was 1500 kg/m3. The plates were modeled using a mesh with 651 nodes, for the rectangular plates, and with 441 nodes, for the square plate. The extensional elastic stiffness constants are shown in Table 2. The terms “Aniso”, “Ortho” and “Quasi-iso” are simplifications of “Anisotropic”, “Orthotropic” and “Quasi-isotropic”, respectively. Only the first fifteen mode shapes were analyzed.
\n\t\t\t
As can be seen in Table 2, the constants A\n\t\t\t\t12 and A\n\t\t\t\t66 for the orthotropic laminates I and IIare equals. They also are equals to laminates with the same characteristics but with 90° unidirectional fibers. 0° and 90° unidirectional laminated plates are only different in relation to A\n\t\t\t\t11 and A\n\t\t\t\t22 terms. These are inverted: A\n\t\t\t\t11 term of the 0° laminate is equal to A\n\t\t\t\t22 term of the 90° laminate, and vice-verse. For the generally orthotropic laminate III and orthotropic laminate IV the difference are only the A\n\t\t\t\t16 and A\n\t\t\t\t26 constants: they are nulls for the laminate IV and non-nulls for the laminate III. For laminate III all extensional elastic constants are non-nulls, similar to fully anisotropic laminates, what, consequently, originates to full extensional elastic stiffness matrix.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Bending elastic constants
\n\t\t\t\t\t\t
N x mm
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
64363.9
\n\t\t\t\t\t\t
0.02
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
24155.8
\n\t\t\t\t\t\t
0.04
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
8875.1
\n\t\t\t\t\t\t
0.02
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
10032.7
\n\t\t\t\t\t\t
1.22
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
6019.6
\n\t\t\t\t\t\t
0.63
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
6019.6
\n\t\t\t\t\t\t
0.64
\n\t\t\t\t\t
\n\t\t\t\t
Table 1.
Bending elastic stiffness constants of the tested anisotropic plate and the computed errors.
\n\t\t\t
The key point of this technique of identification is related with the correct choice of mode shapes together to the weighting functions (virtual fields). The correct mode shapes are called here by “suitable modes” and the correct combination between these modes and the weighting functions are called by “suitable combinations”. The identification of the suitable modes is not difficult, as it will be shown in the next topics. But, the suitable combinations are more difficult because they depend on the type and the geometry of the material. Fortunately, there are some aspects that help finding the best choice. Unlike the bending stiffness identification method originally proposed, for this method there are a lot of modes and suitable combinations that give satisfactory results.
Laminated plates used for the verification of the method
\n\t\t\t
\n\t\t\t\t[90 0 0 45]S anisotropic plate\n\t\t\t
\n\t\t\t
\n\t\t\t\tTable 3 shows some errors computed for the anisotropic plate, rectangular and square. It was considered only the first fifteen in-plane modes shapes. Anisotropic plates, in general, give very satisfactory results using the combinations among suitable modes. This factor can be justified by the fact of these combinations be hardly involved with all required extensional elastic constants A\n\t\t\t\tij’s.
\n\t\t\t
The numerical contribution of each mode to the computation of a specific constant cannot be jeopardized by numerical contribution of another mode during the solution of the system given by Eq. (40).The suitable modes are those that when associated with weighting functions do not null or give very low values for integrals of the right (K matrix) and/or left (C matrix) hand sides of Eq. (40). The suitable combinations are one composed by suitable modes and that give more accurate results. In the majority of the cases, combinations using a higher number of suitable modes can be suitable combinations. According to Table 3 is possible to see that using combinations with only two suitable modes very satisfactory results can be obtained. Satisfactory results would also be obtained using combinations with any modes since the number of suitable modes among all used modes is higher than non-suitable modes. But the accuracy of these results cannot be guaranteed for all combinations.
In general, for the orthotropic and isotropic materials is more difficult to find the suitable combinations when it is compared to fully anisotropic materials. It is necessary to take care to correctly identifying the combinations that give the best results. In these types of materials not all combinations are among suitable modes that can be considered as being suitable combinations. According to values found to terms of the K and C matrices, Eq. (40), and using combinations among suitable modes, it is possible to see the following types of systems:
Errors computed for the anisotropic plate using some suitable combinations.
\n\t\t\t
whereI\n\t\t\t\t1, I\n\t\t\t\t2, I\n\t\t\t\t3, I\n\t\t\t\t4, I\n\t\t\t\t5, I\n\t\t\t\t6, and I\n\t\t\t\t7 are the integral values of Eq. (40). These integrals can be negatives or positives depending on strain direction and reference coordinate axis. As can be observed, for these two types of systems, Eq. (42) and Eq. (43), all elastic constants are involved, and, however, combinations associated to only one type of system can be suitable combinations and sufficient to give correct results. For this plate were found the following suitable modes: 2, 3, 6, 8, 11, and 14.
\n\t\t\t
\n\t\t\t\tFor the square plate: for this plate, the suitable modes are: 2, 3, 6, 7, 11, and 12. The systems of equations are full, even though of the additional terms, that are null in rectangular plate, to be low in this square plate. It is observed in this plate that for each suitable mode there is another identical but out-of-phase at 90°: modes 2 and 3, 6 and 7, and, 11 and 12.
\n\t\t\t
\n\t\t\t\tTable 4 shows errors computed to some suitable combinations for these orthotropic plates. As can be seen, very satisfactory results can be obtained using correct combinations of modes. For this type of orthotropy, it can be more difficult to compute an accurate value for constant A\n\t\t\t\t12. The identification of the suitable combinations is not so clear. As this technique of identification is associated to the solution of an equation system having different modal contributions, it is difficult to identify which modes compose a correct combination.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho I rectangular plate – suitable modes: 2, 3, 6, 8, 11, and 14
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3-6-8-11-14
\n\t\t\t\t\t\t
0.14
\n\t\t\t\t\t\t
3.80
\n\t\t\t\t\t\t
0.12
\n\t\t\t\t\t\t
1.22
\n\t\t\t\t\t\t
-2.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3-6-8
\n\t\t\t\t\t\t
0.11
\n\t\t\t\t\t\t
2.90
\n\t\t\t\t\t\t
0.24
\n\t\t\t\t\t\t
0.74
\n\t\t\t\t\t\t
-2.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
3-6-8-11
\n\t\t\t\t\t\t
0.17
\n\t\t\t\t\t\t
1.58
\n\t\t\t\t\t\t
0.31
\n\t\t\t\t\t\t
1.67
\n\t\t\t\t\t\t
-1.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-8-11
\n\t\t\t\t\t\t
0.17
\n\t\t\t\t\t\t
0.29
\n\t\t\t\t\t\t
0.23
\n\t\t\t\t\t\t
1.46
\n\t\t\t\t\t\t
-1.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
6-8-11
\n\t\t\t\t\t\t
0.18
\n\t\t\t\t\t\t
0.89
\n\t\t\t\t\t\t
0.34
\n\t\t\t\t\t\t
1.91
\n\t\t\t\t\t\t
-4.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
1.0 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
3-8
\n\t\t\t\t\t\t
0.02
\n\t\t\t\t\t\t
5.75
\n\t\t\t\t\t\t
0.91
\n\t\t\t\t\t\t
0.13
\n\t\t\t\t\t\t
-1.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
8.4 x 103\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
8-11
\n\t\t\t\t\t\t
0.25
\n\t\t\t\t\t\t
0.42
\n\t\t\t\t\t\t
0.40
\n\t\t\t\t\t\t
2.17
\n\t\t\t\t\t\t
-2.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
1.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho I square plate – suitable modes: 2, 3, 6, 7, 11, and 12
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3-6-7-11-12
\n\t\t\t\t\t\t
0.09
\n\t\t\t\t\t\t
5.81
\n\t\t\t\t\t\t
0.05
\n\t\t\t\t\t\t
1.89
\n\t\t\t\t\t\t
2.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3-6-11
\n\t\t\t\t\t\t
0.10
\n\t\t\t\t\t\t
5.09
\n\t\t\t\t\t\t
0.06
\n\t\t\t\t\t\t
1.92
\n\t\t\t\t\t\t
-4.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-8.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
3-6-7-12
\n\t\t\t\t\t\t
0.38
\n\t\t\t\t\t\t
2.33
\n\t\t\t\t\t\t
0.08
\n\t\t\t\t\t\t
2.92
\n\t\t\t\t\t\t
6.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-6-11
\n\t\t\t\t\t\t
0.13
\n\t\t\t\t\t\t
5.47
\n\t\t\t\t\t\t
0.11
\n\t\t\t\t\t\t
2.51
\n\t\t\t\t\t\t
-1.0 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-7-12
\n\t\t\t\t\t\t
0.22
\n\t\t\t\t\t\t
5.37
\n\t\t\t\t\t\t
0.04
\n\t\t\t\t\t\t
1.95
\n\t\t\t\t\t\t
1.1 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.5 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-11
\n\t\t\t\t\t\t
0.02
\n\t\t\t\t\t\t
9.04
\n\t\t\t\t\t\t
0.18
\n\t\t\t\t\t\t
0.56
\n\t\t\t\t\t\t
-1.3 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.9 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
6-11
\n\t\t\t\t\t\t
0.18
\n\t\t\t\t\t\t
5.63
\n\t\t\t\t\t\t
0.30
\n\t\t\t\t\t\t
3.46
\n\t\t\t\t\t\t
-1.1 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-2.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
Table 4.
Errors computed for the ortho I plate using some suitable combinations.
\n\t\t\t\tFor the rectangular plate: for this plate, modes 3, 10, 11, and 14 originate systems of type 1, Eq. (42), and modes 2, 5, 9, and 15 originate systems of type 2, Eq. (43).
\n\t\t\t
\n\t\t\t\tFor the square plate: for this plate, modes 4, 10, 12, and 14 originate systems of type 1, Eq. (51), and modes 2, 5, 9, and 13 originate systems of the type 2, Eq. (43).
\n\t\t\t
\n\t\t\t\tTable 5 shows the errors computed to some suitable combinations for these orthotropic plates. Using correct combinations very satisfactory results can be obtained. Similar to ortho I plate, for this type of orthotropy, constant A\n\t\t\t\t12is more difficult of being accurately computed.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho II rectangular plate – suitable modes: 2, 3, 5, 9, 10, 11, 14, and 15
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3-5
\n\t\t\t\t\t\t
2.77
\n\t\t\t\t\t\t
6.06
\n\t\t\t\t\t\t
0.08
\n\t\t\t\t\t\t
0.38
\n\t\t\t\t\t\t
2.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
11-14-15
\n\t\t\t\t\t\t
1.14
\n\t\t\t\t\t\t
2.15
\n\t\t\t\t\t\t
0.92
\n\t\t\t\t\t\t
1.15
\n\t\t\t\t\t\t
2.3 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.1 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3
\n\t\t\t\t\t\t
2.36
\n\t\t\t\t\t\t
0.57
\n\t\t\t\t\t\t
0.19
\n\t\t\t\t\t\t
0.72
\n\t\t\t\t\t\t
1.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-10
\n\t\t\t\t\t\t
2.10
\n\t\t\t\t\t\t
0.82
\n\t\t\t\t\t\t
0.60
\n\t\t\t\t\t\t
2.42
\n\t\t\t\t\t\t
-2.0 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.4 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-14
\n\t\t\t\t\t\t
2.04
\n\t\t\t\t\t\t
5.22
\n\t\t\t\t\t\t
0.37
\n\t\t\t\t\t\t
1.12
\n\t\t\t\t\t\t
-3.9 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
11-14
\n\t\t\t\t\t\t
1.64
\n\t\t\t\t\t\t
2.14
\n\t\t\t\t\t\t
0.87
\n\t\t\t\t\t\t
0.98
\n\t\t\t\t\t\t
-1.8 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho II square plate – suitable modes: 2, 4, 5, 9, 10, 12, 13, and 14
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-5
\n\t\t\t\t\t\t
4.13
\n\t\t\t\t\t\t
8.63
\n\t\t\t\t\t\t
0.39
\n\t\t\t\t\t\t
0.45
\n\t\t\t\t\t\t
-3.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-14
\n\t\t\t\t\t\t
2.43
\n\t\t\t\t\t\t
0.78
\n\t\t\t\t\t\t
0.72
\n\t\t\t\t\t\t
2.89
\n\t\t\t\t\t\t
4.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
1.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4
\n\t\t\t\t\t\t
3.35
\n\t\t\t\t\t\t
0.10
\n\t\t\t\t\t\t
0.21
\n\t\t\t\t\t\t
1.25
\n\t\t\t\t\t\t
-3.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-14
\n\t\t\t\t\t\t
1.63
\n\t\t\t\t\t\t
1.59
\n\t\t\t\t\t\t
1.30
\n\t\t\t\t\t\t
4.72
\n\t\t\t\t\t\t
1.1 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.3 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
5-14
\n\t\t\t\t\t\t
2.67
\n\t\t\t\t\t\t
13.54
\n\t\t\t\t\t\t
2.21
\n\t\t\t\t\t\t
2.82
\n\t\t\t\t\t\t
5.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-1.0 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
9-14
\n\t\t\t\t\t\t
2.12
\n\t\t\t\t\t\t
62.05
\n\t\t\t\t\t\t
0.85
\n\t\t\t\t\t\t
3.89
\n\t\t\t\t\t\t
1.1 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.2 x 105\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
Table 5.
Errors computed for the ortho II plate using some suitable combinations.
For these plates, rectangular and square the computed matrices K and C, Eq.(40), are full matrices, similar ones of the anisotropic plates. Thus, the majority of combinations among suitable modes are suitable combinations. Combinations that are not suitable present high errors for all constants, what, consequently, make them easy to be identified. Table 6 shows the errors computed to some suitable combinations. Using correct combinations very satisfactory results can be obtained.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho III rectangular plate – suitable modes: 2, 3, 6, 8, 10, 12, and 13
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
3-6-12
\n\t\t\t\t\t\t
0.25
\n\t\t\t\t\t\t
0.51
\n\t\t\t\t\t\t
0.10
\n\t\t\t\t\t\t
1.05
\n\t\t\t\t\t\t
0.69
\n\t\t\t\t\t\t
0.99
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
8-10-12
\n\t\t\t\t\t\t
4.26
\n\t\t\t\t\t\t
5.42
\n\t\t\t\t\t\t
3.67
\n\t\t\t\t\t\t
3.43
\n\t\t\t\t\t\t
4.60
\n\t\t\t\t\t\t
5.62
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-3
\n\t\t\t\t\t\t
0.85
\n\t\t\t\t\t\t
1.72
\n\t\t\t\t\t\t
1.22
\n\t\t\t\t\t\t
1.39
\n\t\t\t\t\t\t
0.10
\n\t\t\t\t\t\t
0.96
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
3-6
\n\t\t\t\t\t\t
0.63
\n\t\t\t\t\t\t
0.32
\n\t\t\t\t\t\t
0.04
\n\t\t\t\t\t\t
0.22
\n\t\t\t\t\t\t
0.53
\n\t\t\t\t\t\t
0.14
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
6-12
\n\t\t\t\t\t\t
0.71
\n\t\t\t\t\t\t
1.06
\n\t\t\t\t\t\t
0.05
\n\t\t\t\t\t\t
1.39
\n\t\t\t\t\t\t
1.19
\n\t\t\t\t\t\t
1.30
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
10-13
\n\t\t\t\t\t\t
4.42
\n\t\t\t\t\t\t
2.05
\n\t\t\t\t\t\t
0.71
\n\t\t\t\t\t\t
4.07
\n\t\t\t\t\t\t
5.21
\n\t\t\t\t\t\t
0.63
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho III square plate – suitable modes: 2, 4, 6, 8, 9, 12, and 13
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-6
\n\t\t\t\t\t\t
2.62
\n\t\t\t\t\t\t
3.94
\n\t\t\t\t\t\t
3.18
\n\t\t\t\t\t\t
0.59
\n\t\t\t\t\t\t
2.02
\n\t\t\t\t\t\t
3.23
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-8
\n\t\t\t\t\t\t
1.20
\n\t\t\t\t\t\t
2.40
\n\t\t\t\t\t\t
1.64
\n\t\t\t\t\t\t
1.27
\n\t\t\t\t\t\t
0.11
\n\t\t\t\t\t\t
1.19
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4
\n\t\t\t\t\t\t
2.35
\n\t\t\t\t\t\t
1.11
\n\t\t\t\t\t\t
0.02
\n\t\t\t\t\t\t
5.46
\n\t\t\t\t\t\t
4.26
\n\t\t\t\t\t\t
2.90
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-6
\n\t\t\t\t\t\t
0.76
\n\t\t\t\t\t\t
2.76
\n\t\t\t\t\t\t
3.52
\n\t\t\t\t\t\t
0.01
\n\t\t\t\t\t\t
0.53
\n\t\t\t\t\t\t
2.90
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-13
\n\t\t\t\t\t\t
1.75
\n\t\t\t\t\t\t
2.75
\n\t\t\t\t\t\t
1.51
\n\t\t\t\t\t\t
1.92
\n\t\t\t\t\t\t
0.33
\n\t\t\t\t\t\t
1.25
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
12-13
\n\t\t\t\t\t\t
3.08
\n\t\t\t\t\t\t
2.41
\n\t\t\t\t\t\t
2.63
\n\t\t\t\t\t\t
0.53
\n\t\t\t\t\t\t
1.85
\n\t\t\t\t\t\t
2.54
\n\t\t\t\t\t
\n\t\t\t\t
Table 6.
Errors computed for the ortho III plate using some suitable combinations.
\n\t\t\t\tFor the rectangular plate: it was found the following suitable modes: 2, 4, 5, 8, 11, 12 and 14. For this plate, the majority of combinations among the suitable modes are suitable combinations.
\n\t\t\t
\n\t\t\t\tFor the square plate: it was found the following suitable modes:1, 4, 6, 9, 11, 12, and 14. Similar to rectangular plate, here the most of combinations among the suitable modes are suitable combinations.
\n\t\t\t
\n\t\t\t\tTable 7 shows errors computed to some suitable combinations. Using correct combinations, very satisfactory results can be obtained.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho IV rectangular plate – suitable modes: 2, 4, 5, 8, 11, 12, and 14
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-5
\n\t\t\t\t\t\t
1.52
\n\t\t\t\t\t\t
2.15
\n\t\t\t\t\t\t
1.28
\n\t\t\t\t\t\t
1.54
\n\t\t\t\t\t\t
-1.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.6 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4-8
\n\t\t\t\t\t\t
1.50
\n\t\t\t\t\t\t
2.09
\n\t\t\t\t\t\t
0.83
\n\t\t\t\t\t\t
1.14
\n\t\t\t\t\t\t
1.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.9 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
5-11-12
\n\t\t\t\t\t\t
0.27
\n\t\t\t\t\t\t
0.09
\n\t\t\t\t\t\t
0.04
\n\t\t\t\t\t\t
1.11
\n\t\t\t\t\t\t
-1.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
1.9 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-4
\n\t\t\t\t\t\t
1.18
\n\t\t\t\t\t\t
1.83
\n\t\t\t\t\t\t
1.02
\n\t\t\t\t\t\t
2.87
\n\t\t\t\t\t\t
-1.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
2-5
\n\t\t\t\t\t\t
0.49
\n\t\t\t\t\t\t
1.01
\n\t\t\t\t\t\t
1.01
\n\t\t\t\t\t\t
1.41
\n\t\t\t\t\t\t
-1.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
-0.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
5-11
\n\t\t\t\t\t\t
0.90
\n\t\t\t\t\t\t
0.37
\n\t\t\t\t\t\t
0.04
\n\t\t\t\t\t\t
1.05
\n\t\t\t\t\t\t
3.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ortho IV square plate – suitable modes: 1, 4, 6, 9, 11, 12, and 14
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Suitable combinations
\n\t\t\t\t\t\t
Errors (%)
\n\t\t\t\t\t\t
Differences (N/m)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t11\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t12\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t22\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t66\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t16\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t26\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
1-6-12
\n\t\t\t\t\t\t
0.16
\n\t\t\t\t\t\t
0.30
\n\t\t\t\t\t\t
0.13
\n\t\t\t\t\t\t
3.07
\n\t\t\t\t\t\t
1.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
2.5 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
6-9-12
\n\t\t\t\t\t\t
0.18
\n\t\t\t\t\t\t
0.35
\n\t\t\t\t\t\t
0.30
\n\t\t\t\t\t\t
2,68
\n\t\t\t\t\t\t
1.3 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
4.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
9-12-14
\n\t\t\t\t\t\t
0.18
\n\t\t\t\t\t\t
1.87
\n\t\t\t\t\t\t
0.40
\n\t\t\t\t\t\t
0.68
\n\t\t\t\t\t\t
-6.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
8.1 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
1-12
\n\t\t\t\t\t\t
0.59
\n\t\t\t\t\t\t
0.26
\n\t\t\t\t\t\t
0.74
\n\t\t\t\t\t\t
2.79
\n\t\t\t\t\t\t
2.0 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
2.9 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
4-11
\n\t\t\t\t\t\t
0.94
\n\t\t\t\t\t\t
1.55
\n\t\t\t\t\t\t
2.77
\n\t\t\t\t\t\t
0.23
\n\t\t\t\t\t\t
2.2 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
0.8 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
12-14
\n\t\t\t\t\t\t
0.26
\n\t\t\t\t\t\t
2.17
\n\t\t\t\t\t\t
0.19
\n\t\t\t\t\t\t
0.90
\n\t\t\t\t\t\t
-9.7 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
9.4 x 104\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
Table 7.
Errors computed for the ortho IV plate using some suitable combinations.
\n\t\t\t\tFor the rectangular plate: it was found the following suitable modes: 1, 4, 6, 8, 11, 12, and 14. For this plate the most of combinations among the suitable modes are suitable combinations.
\n\t\t\t
\n\t\t\t\tFor the square plate: it was found the following suitable modes: 2, 3, 7, 8, 10, and 11. Similar to rectangular plate, here the majority of combinations among the suitable modes are suitable combinations.
\n\t\t\t
\n\t\t\t\tTable 8 shows errors computed to some suitable combinations. Using correct combinations, very satisfactory results can be obtained.
Errors computed for the quasi-isotropic plate using some suitable combinations.
\n\t\t\t
\n\t\t\t\tFigs. 3 to 14 show the fifteen first in-plane mode shapes to all the analyzed plates: rectangular and square geometry.
\n\t\t\t
Figure 3.
Fifteen first in-plane mode shapes and natural frequencies to anisotropic rectangular plate.
\n\t\t\t
Figure 4.
Fifteen first in-plane mode shapes and natural frequencies to anisotropic square plate.
\n\t\t\t
Figure 5.
Fifteen first in-plane mode shapes and natural frequencies to ortho I rectangular plate.
\n\t\t\t
Figure 6.
Fifteen first in-plane mode shapes and natural frequencies to ortho I square plate.
\n\t\t\t
Figure 7.
Fifteen first in-plane mode shapes and natural frequencies to ortho II rectangular plate.
\n\t\t\t
Figure 8.
Fifteen first in-plane mode shapes and natural frequencies to ortho II square plate.
\n\t\t\t
Figure 9.
Fifteen first in-plane mode shapes and natural frequencies to ortho III rectangular plate.
\n\t\t\t
Figure 10.
Fifteen first in-plane mode shapes and natural frequencies to ortho III square plate.
\n\t\t\t
Figure 11.
Fifteen first in-plane mode shapes and natural frequencies to ortho IV rectangular plate.
\n\t\t\t
Figure 12.
Fifteen first in-plane mode shapes and natural frequencies to ortho IV square plate.
\n\t\t\t
Figure 13.
Fifteen first in-plane mode shapes and natural frequencies to quasi-iso rectangular plate.
\n\t\t\t
Figure 14.
Fifteen first in-plane mode shapes and natural frequencies to quasi-iso square plate.
\n\t\t
\n\t\t
\n\t\t\t
4. Conclusions
\n\t\t\t
The identification of elastic properties using VFM has shown to be a very efficient technique since the correct combinations among mode shapes and weighing functions are used. This factor is the key point to find the correct results. However, the identification of these suitable combinations is not so simple in some situations, mainly to the extensional elastic stiffness identification method. Fortunately, there are some characteristics that can help to find such combinations, as it was shown here. A great advantage of this method is related to the large number of possibilities to make combinations able to give very satisfactory results.
\n\t\t
\n\t\n',keywords:",",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/16972.pdf",chapterXML:"https://mts.intechopen.com/source/xml/16972.xml",downloadPdfUrl:"/chapter/pdf-download/16972",previewPdfUrl:"/chapter/pdf-preview/16972",totalDownloads:2610,totalViews:159,totalCrossrefCites:0,totalDimensionsCites:0,totalAltmetricsMentions:0,introChapter:null,impactScore:0,impactScorePercentile:27,impactScoreQuartile:2,hasAltmetrics:0,dateSubmitted:"October 27th 2010",dateReviewed:"May 6th 2011",datePrePublished:null,datePublished:"August 23rd 2011",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/16972",risUrl:"/chapter/ris/16972",book:{id:"1046",slug:"nanocomposites-with-unique-properties-and-applications-in-medicine-and-industry"},signatures:"Fabiano Bianchini Batista and Éder Lima de Albuquerque",authors:[{id:"31429",title:"Dr.",name:"Fabiano",middleName:"Bianchini",surname:"Batista",fullName:"Fabiano Batista",slug:"fabiano-batista",email:"fabianchini@ufsj.edu.br",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"Federal University of São João del-Rei",institutionURL:null,country:{name:"Brazil"}}},{id:"41922",title:"Dr.",name:"Éder Lima",middleName:null,surname:"Albuquerque",fullName:"Éder Lima Albuquerque",slug:"eder-lima-albuquerque",email:"ederlima@fem.unicamp.br",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Identification of elastic constants using VFM",level:"1"},{id:"sec_2_2",title:"2.1. Review of the Virtual Fields Method - VFM",level:"2"},{id:"sec_3_2",title:"2.2. Review of the identification method of bending elastic stiffness matrix",level:"2"},{id:"sec_4_2",title:"2.3. Identification method of the extensional elastic stiffness matrix",level:"2"},{id:"sec_4_3",title:"2.3.1. Choice of the weighting functions",level:"3"},{id:"sec_7",title:"3. Results and comments",level:"1"},{id:"sec_8",title:"4. 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Federal University of São João Del ReiUniversity of Brasília, Brazil
'},{corresp:null,contributorFullName:"Éder Lima de Albuquerque",address:null,affiliation:'
Federal University of São João Del ReiUniversity of Brasília, Brazil
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1. Introduction
The dream of harnessing energy from controlled nuclear fusion has been proposed for several decades. Intensifying climate change issues increase the desire for a clean and safe energy source. A fusion reactor based on magnetic confinement provides a promising configuration for controlled thermonuclear fusion. To fuse nuclei with large densities for an extended period, it is necessary to heat the plasma to overcome the Coulomb repulsion. The power ratio, Q, of the fusion output power to the input power is proportional to the fusion product nTτE, where n and T are the central ion density and temperature [1]. The parameter τE is the energy confinement time. In December 2021, the Joint European Torus (JET) achieved a new record and produced 59 MJ of energy with a Q of 0.33 over a τE of 5 s [2]. Although remarkable progress has been made to achieve the required n, T, and τE, they have not been achieved in the same reactor configuration simultaneously.
To achieve an ignition condition where self-sustaining fusion is possible, additional energy-efficient heating is required. Ohmic heating from the toroidal current wanes at high temperatures. Two external sources are typically used to provide heating power, the resonant absorption of radio frequency electromagnetic waves and the injection of energetic neutral particle beams.
The injected beams are neutralized to prevent reflection due to the magnetic field. The neutralization process introduces inefficiency and complicates the instrumentation.
Alternatives to neutral particle beam injection, typically for non-equilibrium fusion reactors, have been explored using different acceleration technologies [3, 4]. The challenges of energy efficiency in particle acceleration are formidable given the high fraction of input power needed to operate relatively low-Q fusion reactors. Radio-frequency acceleration cavities and time-varying electromagnetic fields are, in general, prone to internal ohmic losses and self-heating. Static accelerating fields avoid the bulk of these losses, but are suited primarily for charged particle beams. By construction, the insertion and extraction of charged particles from magnetic confinement systems is thwarted except when necessary, as in the case of divertors. However, non-confining trajectories can be constructed under special conditions through the same processes of cyclotron orbit drift that plague steady-state operation.
In the transverse drift electromagnetic filter developed for the PTOLEMY experiment (Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield), a compact configuration of electromagnetic fields simultaneously transports and decelerates energetic electrons from the tritium β-decay endpoint starting in high magnetic fields of several Tesla to regions where both the kinetic energy and magnetic fields are reduced by several orders of magnitude [5, 6]. A new method is devised to accelerate low-energy charged particles into a high magnetic field region by operating the PTOLEMY filter in “reverse.” This chapter presents the principles of this acceleration method and describes a possible application using the diagnostic port of the International Thermonuclear Experimental Reactor (ITER) [7].
2. Basics of charged particle beam injection
In this chapter, we use the convention that non-bolded symbols of vector quantities refer to the total magnitude unless a component is specified. The equation of motion of a charged particle of mass m and charge q in a magnetic field B is given by
ddtmdrdt=qdrdt×B.E1
The Lorentz force on the right-hand side is perpendicular to the particle’s velocity. In a uniform magnetic field, the particle’s motion projected on a plane perpendicular to the magnetic field is circular, with a gyroradius given by
ρ=mυ⊥qB=2mT⊥qB,E2
with T⊥ the transverse kinetic energy.
For a 1 MeV deuterium ion in a 5 T magnetic field, the gyroradius is about 0.04 m, a small fraction of a typical reactor radius. The ion beam injection energies must be relativistic to be commensurate with the reactor radius.
Relativistic ion beam injection introduces a number of inefficiencies. The plasma does not have the density required to stop energetic ions in a single transit, delivering limited power to the plasma and creating destructive irradiation of the reactor walls. The acceleration methods for relativistic beams involve time-varying fields that have several sources of intrinsic power loss.
In the following sections, charged particle injection of non-relativistic ions is re-examined as a transport mechanism that drifts charged ions from outside of the reactor volume to the surface of the plasma.
3. Magnetic orbital angular momentum beam acceleration
An alternative method to inject a charged particle beam is to create a beam of particles whose gyroradius is small compared to the transverse dimensions of the injection aperture. The particles are in cyclotron motion in a magnetic field that is relatively strong compared to their momentum. The acceleration mechanism stems from the ability of particles traveling in cyclotron motion in magnetic field gradients to do work. One, therefore, configures a magnetic geometry such that there is a transverse gradient along the average path of the beam. A complementary electric field is used to balance the gradient-B drift transverse to the average path of the beam and to accelerate the particles under the work of the magnetic field gradient. The acceleration process will be shown to be adiabatic for relevant injection energies and to maintain the magnetic moment invariance to a good accuracy after an initial stage of zero field ion source injection. The acceleration process does not affect the average linear momentum component of the beam. The increase in the charged particle kinetic energy follows from an increase in the magnetic orbital angular momentum.
3.1 Guiding-center drifts in adiabatic field conditions
When a charged particle gyrates in a magnetic field with a transverse gradient, the cyclotron-orbit averaged Guiding Center System (GCS) [8] motion can be described in terms of the drift terms of the virtual guiding-center particle if the spatial and temporal field variations within a single cyclotron orbit are taken to be adiabatic, i.e.,
ρc≪B∇B,E∇E;andE3
τc≪BdB/dt,EdE/dt;E4
where ρc is the Larmor radius and τc the cyclotron period. Under the conditions specified by Eq. (3) and (4), the first adiabatic invariant μ,
μ=mv⊥22B=T⊥B,E5
accurately describes an invariant quantity preserved in the motion of the particle [9, 10] and shows that an increase in the magnetic field magnitude is accompanied by a proportional increase in the transverse kinetic energy. Additionally, the deviation of the GCS trajectory from the direction of the magnetic field lines can be described in terms of four fundamental drift terms,
VD=V⊥=qE+F−μ∇B−mdVdt×BqB2,E6
where V⊥ is the perpendicular component of the GCS velocity with respect to the magnetic field line. The transverse drift velocity, VD, is composed of individual terms, as appear in Eq. (6) from left to right, known as (1) the E × B drift; (2) the external force drift; (3) the gradient-B drift; and (4) the inertial drift [8]. It is possible to configure the electric and magnetic field parameters to manipulate certain drift terms to produce a net linear trajectory in the transverse direction [5].
3.2 Drifts and work
The gradient-B drift is able to drive a charged particle up or down an electrostatic potential. This ability to do work, at first, seems contrary to the notion that magnetic fields do not do work on charged particles, as seen in Eq. (1), from the cross-product. Similarly, under the motion of E × B drift alone, the cross-product bars work as the electrons will drift on surfaces of constant voltage. This can also be understood by considering that it is always possible to boost into a frame in which the E × B drift is zero.
In contrast, a gradient-B drift due to a spatially varying magnetic field implies a time-varying electric field that cannot be boosted to zero. By itself, i.e., with a magnetic field and no electric field, a gradient-B does no work because there is nothing to do work against. However, when accompanied by an external E × B drift, the external electric potential provides a surface against which the gradient-B drift can do work on. The internal rotational kinetic energy of gyromotion of the virtual guiding-center particle is reduced for a corresponding increase in voltage potential. This is described by inserting terms from Eq. (6),
dT⊥dt=−qE⋅VD=−qE⋅qE−μ∇B×BqB2=μB2E⋅∇B×B,E7
where T⊥ is the internal kinetic energy of gyromotion in the GCS frame [8].
3.3 Balanced drift
To produce a filter or accelerator based on the drift terms in Eq. (6), the external force and inertial drift terms are first taken to be zero, leaving only the electric and gradient-B drifts to be configured such that the total net drift is along a straight line parallel to the direction of the magnetic field gradient. The gradient-B drift alone is orthogonal to the direction of the magnetic field gradient, so the first step is to create a component of the E × B drift that exactly counters the gradient-B drift. From Eq. (6), this specifies the requirement,
qE∥×B=μ∇B×B,E8
where E∥ is the component of electric field parallel to the magnetic field gradient. In general, the ratio of the parallel electric field to the magnitude of the magnetic field to meet this condition depends on the ratio μ/q times the fractional rate of change of the transverse component of the magnetic field along the direction of the magnetic field gradient. For an exponentially falling transverse field, the fractional rate of change is 1/λ, the characteristic exponential length scale in units of transverse distance.
To introduce work, the electric field is tilted by adding an additional component, E⊥, that is orthogonal to the direction of the magnetic field gradient. The E⊥ × B drift is what moves the charged particle either against or along the magnetic field gradient. As the components of E∥ and E⊥ are in vacuum, the relationship between the components follows from solving Maxwell’s equations for a set of voltage plates above and below the direction of the balanced drift. Explicit solutions have been found [5]. Given that the magnitudes of E∥ and E⊥ are related, it is not surprising that the net drift velocity along the acceleration direction is constant. There is no linear momentum acceleration present. The acceleration occurs through the increase in the transverse kinetic energy component, the magnetic orbital angular momentum, during a process of constant drift along the magnetic field gradient.
3.4 Performance
Because the orbital magnetic moment μ = T⊥/B is invariant, if the B field increases (or decreases) exponentially along the trajectory of the particle, so must its transverse kinetic energy. Figure 1 shows the trajectory of a deuterium ion in a balanced drift with an initial kinetic energy of 20 keV at 0.2 T, going to a 4.7 T region with 1 MeV final kinetic energy. In this simulation, using CST studio [11], the magnetic field (Figure 2) is scaled from the one produced by the PTOLEMY magnet [6]. The maximum of the Bx field is set to 4.7 T at Z = 1.6 m to match the toroidal field near the interface of the upper port of ITER [12]. The electric field as in Figure 3 is generated by a similar electrode structure as in the PTOLEMY transverse drift filter [6]. The dimensions are scaled up such that the distance between the electrodes is 0.3 m.
Figure 1.
The trajectory of a deuterium ion in a transverse drift accelerator is shown with the low energy ion source on the left at a low magnetic field region and the high energy ion exiting the accelerator on the right in a region of high magnetic field. The net vertical drift is balanced to zero by construction as the ion drifts at constant velocity from left to right while climbing the magnetic field gradient. The trajectory is computed using the CST software suite. The color scale indicates the kinetic energy of the ion increasing from 20 keV at 0.2 T to 1 MeV at 4.7 T.
Figure 2.
The profile of the transverse magnetic field in the CST simulation for the trajectory shown in Figure 1. It is derived from scaling the magnetic field produced by the PTOLEMY magnet to match a maximum Bx of 4.7 T.
Figure 3.
The electric field in the transverse plane in the drift region for the trajectory shown in Figure 1. The color (orientation) of the arrow indicates the magnitude (direction) of the field at its tail-end position.
3.5 Injection
The net drift is along the direction of the magnetic field gradient and drives the guiding-center of the beam to cross equipotential lines and accelerates the particles. As the beam drifts in the direction of ∇B, it naturally reaches its maximum kinetic energy upon entering the toroidal magnet of a tokamak.
Via the foregoing mechanism, initial simulations of injecting deuterium ions indicate successful delivery of the beam, as shown in Figure 4. Once the particle leaves the injection port, the gradient of the 1/R toroidal magnetic field drifts the ions into the center of the plasma. The relatively hot thermal temperature of the 1 MeV deuterium ions will thermalize through Coulomb interactions with the plasma. The injection mechanism supports a range of injection energies and ion species. For instance, injection of 4 MeV α-particles through the ITER diagnostic port may be an effective way of studying the effects of fusion final-state ion interactions on the plasma. Charge neutralization can be achieved by instrumenting ion (electron) injection ports on the top (bottom) of the tokamak. The gradient-B drift will drift ions downward (for a given orientation of the azimuthal toroidal magnetic field) and electrons (or negative ions) upward.
Figure 4.
Simulation of the injection of deuterium ions into a 1/R magnetic field in a tokamak using the accelerating structure of Figure 1. Upon exiting the accelerator, the energetic ion continues to drift toward the plasma confinement region under the 1/R magnetic field gradient-B drift of the tokamak.
The desired injection magnetic field, as described in Ref. [6], can be produced by a tapered dipole magnet with a superconductor winding, as in Figure 5.
Figure 5.
A conceptual design of a tapered dipole magnet winding to generate the desired magnetic field for magnetic orbital angular momentum beam acceleration. The winding of the coils follows the surface of a cylindrical vacuum insertion port, similar to dipole magnets used in circular proton beam accelerators.
A field cage with a number of electrodes can be placed inside the magnet to produce the corresponding electric field. Such a magnet is compact and can be placed within a counter-dipole coil in the upper diagnostic ports of ITER, as shown in Figure 6. The counter-dipole creates a zero field region for the ion source and reduces Lorentz forces on the primary reactor coils. The details of this magnet and the field cage are beyond the scope of this chapter.
Figure 6.
A tapered dipole magnet, as shown in Figure 5, within a counter-dipole winding placed in the upper port between two adjacent ITER toroidal field coils. The counter-dipole reduces the magnetic forces between the injection system and the tokamak field windings.
4. Energy efficiency
An important aspect of magnetic orbital angular momentum acceleration for fusion energy efficiency is the reliance solely on static electric and magnetic fields. The power loading during injection on the accelerating plate voltages draws from highly efficient DC power supplies. Above all, the largest inefficiency of neutral beam injection, the neutralization, is avoided with direct charged particle injection. The high currents and efficient production of positive ions saves on power losses at the source relative to the negative ion beams used for neutral beam injection [13]. The inefficiencies and beam energy limitations associated with neutralization and neutral beam injection introduce approximately a factor of 2 loss in absolute power efficiency [14].
5. Conclusions
Fusion reactor science is on the brink of a major advance toward sustained clean energy reactors. Reducing inefficiency in the particle beam injection systems is a promising direction toward achieving ignition conditions without compromising reactor operation. A surprising and yet potentially revolutionary approach to improving beam heating is through a new particle acceleration method called magnetic orbital angular momentum beam acceleration. With this technique, charged particle beam injection into magnetically confined plasmas becomes possible. The relevant parameters for charged particle beam injection are presented with simulated geometries demonstrating the feasibility of implementing this system with the diagnostic port of ITER. Charged particle beam injection provides a new tool for fusion reactors to deliver charge, mass, and heat flow into the plasma. The large gain in energy efficiency for charged particle injection is the most advantageous factor in comparing with neutral beam injection.
Acknowledgments
This research was supported by the Simons Foundation (#377485) and the John Templeton Foundation (#61814).
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Accelerator based fusion reactor. Nuclear Fusion. 2017;57(8):084002'},{id:"B4",body:'Labaune C, Baccou C, Depierreux S, Goyon C, Loisel G, Yahia V, et al. Fusion reactions initiated by laser-accelerated particle beams in a laser-produced plasma. Nature Communications. 2013;4(1):1-6'},{id:"B5",body:'Betti MG, Biasotti M, Bosca A, Calle F, Carabe-Lopez J, Cavoto G, et al. A design for an electromagnetic filter for precision energy measurements at the tritium endpoint. Progress in Particle and Nuclear Physics. 2019;106:120-131'},{id:"B6",body:'Apponi A, Betti MG, Borghesi M, Canci N, Cavoto G, Chang C, et al. Implementation and optimization of the PTOLEMY transverse drift electromagnetic filter. Journal of Instrumentation. 2022;17(05):P05021. DOI: 10.1088/1748-0221/17/05/p05021'},{id:"B7",body:'International Thermonuclear Experimental Reactor (ITER). 2022. Available from: http://www.iter.org [Accessed: 2022-06]'},{id:"B8",body:'Roederer J, Zhang H. Particle fluxes, distribution functions and violation of invariants. In: Dynamics of Magnetically Trapped Particles. Berlin, Heidelberg: Springer-Verlag; 2014. pp. 89-122. Available online: https://link.springer.com/book/10.1007/978-3-642-41530-2#bibliographic-information'},{id:"B9",body:'Alfvén H. On the motion of a charged particle in a magnetic field. Arkiv foer Matematik, Astronomi, och Fysik. 1940;25B(1–20):29'},{id:"B10",body:'Cary JR, Brizard AJ. Hamiltonian theory of guiding-center motion. Reviews of Modern Physics. 2009;81(2):693'},{id:"B11",body:'Dassault Systèmes. CST Studio Suite; Available from: http://www.cst.com'},{id:"B12",body:'International Atomic Energy Agency. Summary of the ITER Final Design Report. No. 22 in ITER EDA Documentation Series. Vienna: International Atomic Energy Agency; 2001. Available from: https://www.iaea.org/publications/6442/summary-of-the-iter-final-design-report'},{id:"B13",body:'Hemsworth RS, Inoue T. Positive and negative ion sources for magnetic fusion. IEEE Transactions on Plasma Science. 2005;33(6):1799-1813'},{id:"B14",body:'Hopf C, Starnella G, den Harder N, Fantz U. Neutral beam injection for fusion reactors: Technological constraints versus functional requirements. Nuclear Fusion. 2021;61(10):106032. DOI: 10.1088/1741-4326/ac227a'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Wonyong Chung",address:null,affiliation:'
Department of Physics, Princeton University, Princeton, New Jersey, USA
Department of Physics, Princeton University, Princeton, New Jersey, USA
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7.4 Waiver: No failure or delay by a party to exercise any right or remedy provided under this Publication Agreement or by law shall constitute a waiver of that or any other right or remedy, nor shall it preclude or restrict the further exercise of that or any other right or remedy. No single or partial exercise of such right or remedy shall preclude or restrict the further exercise of that or any other right or remedy.
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7.5 Variation: No variation of this Publication Agreement shall be effective unless it is in writing and signed by the parties (or their duly authorized representatives).
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7.6 Severance: If any provision or part-provision of this Publication Agreement is or becomes invalid, illegal or unenforceable, it shall be deemed modified to the minimum extent necessary to make it valid, legal and enforceable. If such modification is not possible, the relevant provision or part-provision shall be deemed deleted.
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Any modification to or deletion of a provision or part-provision under this clause shall not affect the validity and enforceability of the rest of this Publication Agreement.
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7.7 No partnership: Nothing in this Publication Agreement is intended to, or shall be deemed to, establish or create any partnership or joint venture or the relationship of principal and agent or employer and employee between IntechOpen and the Corresponding Author or any Co-Author, nor authorize any party to make or enter into any commitments for or on behalf of any other party.
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7.8 Governing law: This Publication Agreement and any dispute or claim (including non-contractual disputes or claims) arising out of or in connection with it or its subject matter or formation shall be governed by and construed in accordance with the law of England and Wales. The parties submit to the exclusive jurisdiction of the English courts to settle any dispute or claim arising out of or in connection with this Publication Agreement (including any non-contractual disputes or claims).
The Corresponding Author (acting on behalf of all Authors) and INTECHOPEN LIMITED, incorporated and registered in England and Wales with company number 11086078 and a registered office at 5 Princes Gate Court, London, United Kingdom, SW7 2QJ conclude the following Agreement regarding the publication of a Book Chapter:
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1. DEFINITIONS
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Corresponding Author: The Author of the Chapter who serves as a Signatory to this Agreement. The Corresponding Author acts on behalf of any other Co-Author.
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Co-Author: All other Authors of the Chapter besides the Corresponding Author.
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IntechOpen: IntechOpen Ltd., the Publisher of the Book.
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Book: The publication as a collection of chapters compiled by IntechOpen including the Chapter. Chapter: The original literary work created by Corresponding Author and any Co-Author that is the subject of this Agreement.
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2. CORRESPONDING AUTHOR'S GRANT OF RIGHTS
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2.1 Subject to the following Article, the Corresponding Author grants and shall ensure that each Co-Author grants, to IntechOpen, during the full term of copyright and any extensions or renewals of that term the following:
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An irrevocable, worldwide, royalty-free, perpetual, transferable, sublicensable, non-exclusive right to publish, communicate to the public, reproduce, republish, transmit, sell, distribute and otherwise use and make available the Chapter in whole, partial or adapted from and/or incorporated in or in conjunction with other works, in electronic and print editions of the Publication and in derivative works and on any platform owned and/or operated by IntechOpen, throughout the world, in all languages, and in all media and formats now known or later developed.
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An irrevocable, worldwide, royalty-free, perpetual, transferable, sublicensable, non-exclusive right to create and store electronic archival copies of the Chapter, including the right to deposit the Chapter in open access digital repositories.
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An irrevocable, worldwide, royalty-free, perpetual, transferable, sublicensable, non-exclusive right to license others to reproduce, translate, republish, transmit and distribute the Chapter in whole, partial or adapted from and/or incorporated in or in conjunction with other works under the condition that the Corresponding Author and each Co-Author is attributed (currently this is carried out by publishing the Chapter under a Creative Commons Attribution 3.0 Unported License).
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The aforementioned licenses shall survive the expiry or termination of this Agreement for any reason.
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2.2 The Corresponding Author (on their own behalf and on behalf of any Co-Author) reserves the following rights to the Chapter but agrees not to exercise them in such a way as to adversely affect IntechOpen's ability to utilize the full benefit of this Publication Agreement: (i) reprographic rights worldwide, other than those which subsist in the typographical arrangement of the Chapter as published by IntechOpen; and (ii) public lending rights arising under the Public Lending Right Act 1979, as amended from time to time, and any similar rights arising in any part of the world.
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The Corresponding Author confirms that they (and any Co-Author) are and will remain a member of any applicable licensing and collecting society and any successor to that body responsible for administering royalties for the reprographic reproduction of copyright works.
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Subject to the license granted above, copyright in the Chapter and all versions of it created during IntechOpen's editing process (including the published version) is retained by the Corresponding Author and any Co-Author.
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Subject to the license granted above, the Corresponding Author and any Co-Author retains patent, trademark and other intellectual property rights to the Chapter.
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2.3 All rights granted to IntechOpen in this Article are assignable, sublicensable or otherwise transferrable to third parties without the Corresponding Author's or any Co-Author’s specific approval.
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2.4 The Corresponding Author (on their own behalf and on behalf of each Co-Author) will not assert any rights under the Copyright, Designs and Patents Act 1988 to object to derogatory treatment of the Chapter as a consequence of IntechOpen's changes to the Chapter arising from translation of it, corrections and edits for house style, removal of problematic material and other reasonable edits.
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3. CORRESPONDING AUTHOR'S DUTIES
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3.1 When distributing or re-publishing the Chapter, the Corresponding Author agrees to credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen. The Corresponding Author warrants that each Co-Author will also credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen, when they are distributing or re-publishing the Chapter.
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3.2 When submitting the Chapter, the Corresponding Author agrees to:
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Comply with all instructions and guidelines provided by IntechOpen;
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Produce the Chapter with all due skill, care and diligence, and in accordance with good scientific practice;
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Submit all the corrections in due time as defined during the publishing process schedule.
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The Corresponding Author will be held responsible for the payment of the Open Access Publishing Fees.
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All payments shall be due 30 days from the date of the issued invoice. The Corresponding Author or the payer on the Corresponding Author's and Co-Authors' behalf will bear all banking and similar charges incurred.
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3.3 The Corresponding Author shall obtain in writing all consents necessary for the reproduction of any material in which a third-party right exists, including quotations, photographs and illustrations, in all editions of the Chapter worldwide for the full term of the above licenses, and shall provide to IntechOpen upon request the original copies of such consents for inspection (at IntechOpen's option) or photocopies of such consents.
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The Corresponding Author shall obtain written informed consent for publication from people who might recognize themselves or be identified by others (e.g. from case reports or photographs).
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3.4 The Corresponding Author and any Co-Author shall respect confidentiality rights during and after the termination of this Agreement. The information contained in all correspondence and documents as part of the publishing activity between IntechOpen and the Corresponding Author and any Co-Author are confidential and are intended only for the recipient. The contents may not be disclosed publicly and are not intended for unauthorized use or distribution. Any use, disclosure, copying, or distribution is prohibited and may be unlawful.
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4. CORRESPONDING AUTHOR'S WARRANTY
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4.1 The Corresponding Author represents and warrants that the Chapter does not and will not breach any applicable law or the rights of any third party and, specifically, that the Chapter contains no matter that is defamatory or that infringes any literary or proprietary rights, intellectual property rights, or any rights of privacy. The Corresponding Author warrants and represents that: (i) the Chapter is the original work of themselves and any Co-Author and is not copied wholly or substantially from any other work or material or any other source; (ii) the Chapter has not been formally published in any other peer-reviewed journal or in a book or edited collection, and is not under consideration for any such publication; (iii) they themselves and any Co-Author are qualifying persons under section 154 of the Copyright, Designs and Patents Act 1988; (iv) they themselves and any Co-Author have not assigned and will not during the term of this Publication Agreement purport to assign any of the rights granted to IntechOpen under this Publication Agreement; and (v) the rights granted by this Publication Agreement are free from any security interest, option, mortgage, charge or lien.
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The Corresponding Author also warrants and represents that: (i) they have the full power to enter into this Publication Agreement on their own behalf and on behalf of each Co-Author; and (ii) they have the necessary rights and/or title in and to the Chapter to grant IntechOpen, on behalf of themselves and any Co-Author, the rights and licenses expressed to be granted in this Publication Agreement. If the Chapter was prepared jointly by the Corresponding Author and any Co-Author, the Corresponding Author warrants and represents that: (i) each Co-Author agrees to the submission, license and publication of the Chapter on the terms of this Publication Agreement; and (ii) they have the authority to enter into this Publication Agreement on behalf of and bind each Co-Author. The Corresponding Author shall: (i) ensure each Co-Author complies with all relevant provisions of this Publication Agreement, including those relating to confidentiality, performance and standards, as if a party to this Publication Agreement; and (ii) remain primarily liable for all acts and/or omissions of each such Co-Author.
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The Corresponding Author agrees to indemnify and hold IntechOpen harmless against all liabilities, costs, expenses, damages and losses and all reasonable legal costs and expenses suffered or incurred by IntechOpen arising out of or in connection with any breach of the aforementioned representations and warranties. This indemnity shall not cover IntechOpen to the extent that a claim under it results from IntechOpen's negligence or willful misconduct.
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4.2 Nothing in this Publication Agreement shall have the effect of excluding or limiting any liability for death or personal injury caused by negligence or any other liability that cannot be excluded or limited by applicable law.
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5. TERMINATION
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5.1 IntechOpen has a right to terminate this Publication Agreement for quality, program, technical or other reasons with immediate effect, including without limitation (i) if the Corresponding Author or any Co-Author commits a material breach of this Publication Agreement; (ii) if the Corresponding Author or any Co-Author (being an individual) is the subject of a bankruptcy petition, application or order; or (iii) if the Corresponding Author or any Co-Author (being a company) commences negotiations with all or any class of its creditors with a view to rescheduling any of its debts, or makes a proposal for or enters into any compromise or arrangement with any of its creditors.
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In case of termination, IntechOpen will notify the Corresponding Author, in writing, of the decision.
\n\n
6. INTECHOPEN’S DUTIES AND RIGHTS
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6.1 Unless prevented from doing so by events outside its reasonable control, IntechOpen, in its discretion, agrees to publish the Chapter attributing it to the Corresponding Author and any Co-Author.
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6.2 IntechOpen has the right to use the Corresponding Author’s and any Co-Author’s names and likeness in connection with scientific dissemination, retrieval, archiving, web hosting and promotion and marketing of the Chapter and has the right to contact the Corresponding Author and any Co-Author until the Chapter is publicly available on any platform owned and/or operated by IntechOpen.
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6.3 IntechOpen is granted the authority to enforce the rights from this Publication Agreement, on behalf of the Corresponding Author and any Co-Author, against third parties (for example in cases of plagiarism or copyright infringements). In respect of any such infringement or suspected infringement of the copyright in the Chapter, IntechOpen shall have absolute discretion in addressing any such infringement which is likely to affect IntechOpen's rights under this Publication Agreement, including issuing and conducting proceedings against the suspected infringer.
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7. MISCELLANEOUS
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7.1 Further Assurance: The Corresponding Author shall and will ensure that any relevant third party (including any Co-Author) shall, execute and deliver whatever further documents or deeds and perform such acts as IntechOpen reasonably requires from time to time for the purpose of giving IntechOpen the full benefit of the provisions of this Publication Agreement.
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7.2 Third Party Rights: A person who is not a party to this Publication Agreement may not enforce any of its provisions under the Contracts (Rights of Third Parties) Act 1999.
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7.3 Entire Agreement: This Publication Agreement constitutes the entire agreement between the parties in relation to its subject matter. It replaces and extinguishes all prior agreements, draft agreements, arrangements, collateral warranties, collateral contracts, statements, assurances, representations and undertakings of any nature made by or on behalf of the parties, whether oral or written, in relation to that subject matter. Each party acknowledges that in entering into this Publication Agreement it has not relied upon any oral or written statements, collateral or other warranties, assurances, representations or undertakings which were made by or on behalf of the other party in relation to the subject matter of this Publication Agreement at any time before its signature (together "Pre-Contractual Statements"), other than those which are set out in this Publication Agreement. Each party hereby waives all rights and remedies which might otherwise be available to it in relation to such Pre-Contractual Statements. Nothing in this clause shall exclude or restrict the liability of either party arising out of its pre-contract fraudulent misrepresentation or fraudulent concealment.
\n\n
7.4 Waiver: No failure or delay by a party to exercise any right or remedy provided under this Publication Agreement or by law shall constitute a waiver of that or any other right or remedy, nor shall it preclude or restrict the further exercise of that or any other right or remedy. No single or partial exercise of such right or remedy shall preclude or restrict the further exercise of that or any other right or remedy.
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7.5 Variation: No variation of this Publication Agreement shall be effective unless it is in writing and signed by the parties (or their duly authorized representatives).
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7.6 Severance: If any provision or part-provision of this Publication Agreement is or becomes invalid, illegal or unenforceable, it shall be deemed modified to the minimum extent necessary to make it valid, legal and enforceable. If such modification is not possible, the relevant provision or part-provision shall be deemed deleted.
\n\n
Any modification to or deletion of a provision or part-provision under this clause shall not affect the validity and enforceability of the rest of this Publication Agreement.
\n\n
7.7 No partnership: Nothing in this Publication Agreement is intended to, or shall be deemed to, establish or create any partnership or joint venture or the relationship of principal and agent or employer and employee between IntechOpen and the Corresponding Author or any Co-Author, nor authorize any party to make or enter into any commitments for or on behalf of any other party.
\n\n
7.8 Governing law: This Publication Agreement and any dispute or claim (including non-contractual disputes or claims) arising out of or in connection with it or its subject matter or formation shall be governed by and construed in accordance with the law of England and Wales. The parties submit to the exclusive jurisdiction of the English courts to settle any dispute or claim arising out of or in connection with this Publication Agreement (including any non-contractual disputes or claims).
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Last updated: 2020-11-27
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He worked as a post-doctoral fellow at the Public Health Research Institute (PHRI), Newark, NJ for four years before accepting a three-year faculty position at Brigham Young University-Hawaii. Dr. Engohang-Ndong is a tenured faculty member with the academic rank of Full Professor at Kent State University, Ohio, where he teaches a wide range of biological science courses and pursues his research in medical and environmental microbiology. 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He has an excellent track record in the herpesvirus field, and his group is engaged in clinical research in the field of Epstein-Barr virus diseases. He is the editor of the online Encyclopedia of Environment and he coordinates the Universal Health Coverage education program for the BioHealth Computing Schools of the European Institute of Science.",institutionString:null,institution:{name:"Grenoble Alpes University",country:{name:"France"}}},{id:"131400",title:"Prof.",name:"Alfonso J.",middleName:null,surname:"Rodriguez-Morales",slug:"alfonso-j.-rodriguez-morales",fullName:"Alfonso J. Rodriguez-Morales",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/131400/images/system/131400.png",biography:"Dr. Rodriguez-Morales is an expert in tropical and emerging diseases, particularly zoonotic and vector-borne diseases (especially arboviral diseases). He is the president of the Travel Medicine Committee of the Pan-American Infectious Diseases Association (API), as well as the president of the Colombian Association of Infectious Diseases (ACIN). He is a member of the Committee on Tropical Medicine, Zoonoses, and Travel Medicine of ACIN. He is a vice-president of the Latin American Society for Travel Medicine (SLAMVI) and a Member of the Council of the International Society for Infectious Diseases (ISID). Since 2014, he has been recognized as a Senior Researcher, at the Ministry of Science of Colombia. He is a professor at the Faculty of Medicine of the Fundacion Universitaria Autonoma de las Americas, in Pereira, Risaralda, Colombia. He is an External Professor, Master in Research on Tropical Medicine and International Health, Universitat de Barcelona, Spain. He is also a professor at the Master in Clinical Epidemiology and Biostatistics, Universidad Científica del Sur, Lima, Peru. In 2021 he has been awarded the “Raul Isturiz Award” Medal of the API. Also, in 2021, he was awarded with the “Jose Felix Patiño” Asclepius Staff Medal of the Colombian Medical College, due to his scientific contributions to COVID-19 during the pandemic. He is currently the Editor in Chief of the journal Travel Medicine and Infectious Diseases. His Scopus H index is 47 (Google Scholar H index, 68).",institutionString:"Institución Universitaria Visión de las Américas, Colombia",institution:null},{id:"332819",title:"Dr.",name:"Chukwudi Michael",middleName:"Michael",surname:"Egbuche",slug:"chukwudi-michael-egbuche",fullName:"Chukwudi Michael Egbuche",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/332819/images/14624_n.jpg",biography:"I an Dr. Chukwudi Michael Egbuche. I am a Senior Lecturer in the Department of Parasitology and Entomology, Nnamdi Azikiwe University, Awka.",institutionString:null,institution:{name:"Nnamdi Azikiwe University",country:{name:"Nigeria"}}},{id:"284232",title:"Mr.",name:"Nikunj",middleName:"U",surname:"Tandel",slug:"nikunj-tandel",fullName:"Nikunj Tandel",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/284232/images/8275_n.jpg",biography:'Mr. Nikunj Tandel has completed his Master\'s degree in Biotechnology from VIT University, India in the year of 2012. He is having 8 years of research experience especially in the field of malaria epidemiology, immunology, and nanoparticle-based drug delivery system against the infectious diseases, autoimmune disorders and cancer. He has worked for the NIH funded-International Center of Excellence in Malaria Research project "Center for the study of complex malaria in India (CSCMi)" in collaboration with New York University. The preliminary objectives of the study are to understand and develop the evidence-based tools and interventions for the control and prevention of malaria in different sites of the INDIA. Alongside, with the help of next-generation genomics study, the team has studied the antimalarial drug resistance in India. Further, he has extended his research in the development of Humanized mice for the study of liver-stage malaria and identification of molecular marker(s) for the Artemisinin resistance. At present, his research focuses on understanding the role of B cells in the activation of CD8+ T cells in malaria. Received the CSIR-SRF (Senior Research Fellow) award-2018, FIMSA (Federation of Immunological Societies of Asia-Oceania) Travel Bursary award to attend the IUIS-IIS-FIMSA Immunology course-2019',institutionString:"Nirma University",institution:{name:"Nirma University",country:{name:"India"}}},{id:"334383",title:"Ph.D.",name:"Simone",middleName:"Ulrich",surname:"Ulrich Picoli",slug:"simone-ulrich-picoli",fullName:"Simone Ulrich Picoli",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/334383/images/15919_n.jpg",biography:"Graduated in Pharmacy from Universidade Luterana do Brasil (1999), Master in Agricultural and Environmental Microbiology from Federal University of Rio Grande do Sul (2002), Specialization in Clinical Microbiology from Universidade de São Paulo, USP (2007) and PhD in Sciences in Gastroenterology and Hepatology (2012). She is currently an Adjunct Professor at Feevale University in Medicine and Biomedicine courses and a permanent professor of the Academic Master\\'s Degree in Virology. She has experience in the field of Microbiology, with an emphasis on Bacteriology, working mainly on the following topics: bacteriophages, bacterial resistance, clinical microbiology and food microbiology.",institutionString:null,institution:{name:"Universidade Feevale",country:{name:"Brazil"}}},{id:"229220",title:"Dr.",name:"Amjad",middleName:"Islam",surname:"Aqib",slug:"amjad-aqib",fullName:"Amjad Aqib",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/229220/images/system/229220.png",biography:"Dr. Amjad Islam Aqib obtained a DVM and MSc (Hons) from University of Agriculture Faisalabad (UAF), Pakistan, and a PhD from the University of Veterinary and Animal Sciences Lahore, Pakistan. Dr. Aqib joined the Department of Clinical Medicine and Surgery at UAF for one year as an assistant professor where he developed a research laboratory designated for pathogenic bacteria. Since 2018, he has been Assistant Professor/Officer in-charge, Department of Medicine, Manager Research Operations and Development-ORIC, and President One Health Club at Cholistan University of Veterinary and Animal Sciences, Bahawalpur, Pakistan. He has nearly 100 publications to his credit. His research interests include epidemiological patterns and molecular analysis of antimicrobial resistance and modulation and vaccine development against animal pathogens of public health concern.",institutionString:"Cholistan University of Veterinary and Animal Sciences",institution:{name:"University of Agriculture Faisalabad",country:{name:"Pakistan"}}},{id:"333753",title:"Dr.",name:"Rais",middleName:null,surname:"Ahmed",slug:"rais-ahmed",fullName:"Rais Ahmed",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/333753/images/20168_n.jpg",biography:null,institutionString:null,institution:{name:"University of Agriculture Faisalabad",country:{name:"Pakistan"}}},{id:"62900",title:"Prof.",name:"Fethi",middleName:null,surname:"Derbel",slug:"fethi-derbel",fullName:"Fethi Derbel",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62900/images/system/62900.jpeg",biography:"Professor Fethi Derbel was born in 1960 in Tunisia. He received his medical degree from the Sousse Faculty of Medicine at Sousse, University of Sousse, Tunisia. He completed his surgical residency in General Surgery at the University Hospital Farhat Hached of Sousse and was a member of the Unit of Liver Transplantation in the University of Rennes, France. He then worked in the Department of Surgery at the Sahloul University Hospital in Sousse. Professor Derbel is presently working at the Clinique les Oliviers, Sousse, Tunisia. His hospital activities are mostly concerned with laparoscopic, colorectal, pancreatic, hepatobiliary, and gastric surgery. He is also very interested in hernia surgery and performs ventral hernia repairs and inguinal hernia repairs. He has been a member of the GREPA and Tunisian Hernia Society (THS). During his residency, he managed patients suffering from diabetic foot, and he was very interested in this pathology. For this reason, he decided to coordinate a book project dealing with the diabetic foot. Professor Derbel has published many articles in journals and collaborates intensively with IntechOpen Access Publisher as an editor.",institutionString:"Clinique les Oliviers",institution:null},{id:"300144",title:"Dr.",name:"Meriem",middleName:null,surname:"Braiki",slug:"meriem-braiki",fullName:"Meriem Braiki",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/300144/images/system/300144.jpg",biography:"Dr. Meriem Braiki is a specialist in pediatric surgeon from Tunisia. She was born in 1985. She received her medical degree from the University of Medicine at Sousse, Tunisia. She achieved her surgical residency training periods in Pediatric Surgery departments at University Hospitals in Monastir, Tunis and France.\r\nShe is currently working at the Pediatric surgery department, Sidi Bouzid Hospital, Tunisia. Her hospital activities are mostly concerned with laparoscopic, parietal, urological and digestive surgery. She has published several articles in diffrent journals.",institutionString:"Sidi Bouzid Regional Hospital",institution:null},{id:"229481",title:"Dr.",name:"Erika M.",middleName:"Martins",surname:"de Carvalho",slug:"erika-m.-de-carvalho",fullName:"Erika M. de Carvalho",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/229481/images/6397_n.jpg",biography:null,institutionString:null,institution:{name:"Oswaldo Cruz Foundation",country:{name:"Brazil"}}},{id:"186537",title:"Prof.",name:"Tonay",middleName:null,surname:"Inceboz",slug:"tonay-inceboz",fullName:"Tonay Inceboz",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/186537/images/system/186537.jfif",biography:"I was graduated from Ege University of Medical Faculty (Turkey) in 1988 and completed his Med. PhD degree in Medical Parasitology at the same university. I became an Associate Professor in 2008 and Professor in 2014. I am currently working as a Professor at the Department of Medical Parasitology at Dokuz Eylul University, Izmir, Turkey.\n\nI have given many lectures, presentations in different academic meetings. I have more than 60 articles in peer-reviewed journals, 18 book chapters, 1 book editorship.\n\nMy research interests are Echinococcus granulosus, Echinococcus multilocularis (diagnosis, life cycle, in vitro and in vivo cultivation), and Trichomonas vaginalis (diagnosis, PCR, and in vitro cultivation).",institutionString:"Dokuz Eylül University",institution:{name:"Dokuz Eylül University",country:{name:"Turkey"}}},{id:"71812",title:"Prof.",name:"Hanem Fathy",middleName:"Fathy",surname:"Khater",slug:"hanem-fathy-khater",fullName:"Hanem Fathy Khater",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/71812/images/1167_n.jpg",biography:"Prof. Khater is a Professor of Parasitology at Benha University, Egypt. She studied for her doctoral degree, at the Department of Entomology, College of Agriculture, Food and Natural Resources, University of Missouri, Columbia, USA. She has completed her Ph.D. degrees in Parasitology in Egypt, from where she got the award for “the best scientific Ph.D. dissertation”. She worked at the School of Biological Sciences, Bristol, England, the UK in controlling insects of medical and veterinary importance as a grant from Newton Mosharafa, the British Council. Her research is focused on searching of pesticides against mosquitoes, house flies, lice, green bottle fly, camel nasal botfly, soft and hard ticks, mites, and the diamondback moth as well as control of several parasites using safe and natural materials to avoid drug resistances and environmental contamination.",institutionString:null,institution:{name:"Banha University",country:{name:"Egypt"}}},{id:"99780",title:"Prof.",name:"Omolade",middleName:"Olayinka",surname:"Okwa",slug:"omolade-okwa",fullName:"Omolade Okwa",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/99780/images/system/99780.jpg",biography:"Omolade Olayinka Okwa is presently a Professor of Parasitology at Lagos State University, Nigeria. She has a PhD in Parasitology (1997), an MSc in Cellular Parasitology (1992), and a BSc (Hons) Zoology (1990) all from the University of Ibadan, Nigeria. She teaches parasitology at the undergraduate and postgraduate levels. 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She is a reviewer for several local and international journals such as Unilag Journal of Science, Libyan Journal of Medicine, Journal of Medicine and Medical Sciences, and Annual Research and Review in Science. \nShe has authored 45 scientific research publications in local and international journals, 8 scientific reviews, 4 books, and 3 book chapters, which includes the books “Malaria Parasites” and “Malaria” which are IntechOpen access publications.",institutionString:"Lagos State University",institution:{name:"Lagos State University",country:{name:"Nigeria"}}},{id:"273100",title:"Dr.",name:"Vijay",middleName:null,surname:"Gayam",slug:"vijay-gayam",fullName:"Vijay Gayam",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/273100/images/system/273100.jpeg",biography:"Dr. Vijay Bhaskar Reddy Gayam is currently practicing as an internist at Interfaith Medical Center in Brooklyn, New York, USA. 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Fungal infectious illness prevalence and prognosis are determined by the exposure between fungi and host, host immunological state, fungal virulence, and early and accurate diagnosis and treatment. \r\nPatients with both congenital and acquired immunodeficiency are more likely to be infected with opportunistic mycosis. Fungal infectious disease outbreaks are common during the post- disaster rebuilding era, which is characterised by high population density, migration, and poor health and medical conditions.\r\nSystemic or local fungal infection is mainly associated with the fungi directly inhaled or inoculated in the environment during the disaster. The most common fungal infection pathways are human to human (anthropophilic), animal to human (zoophilic), and environment to human (soilophile). Diseases are common as a result of widespread exposure to pathogenic fungus dispersed into the environment. \r\nFungi that are both common and emerging are intertwined. In Southeast Asia, for example, Talaromyces marneffei is an important pathogenic thermally dimorphic fungus that causes systemic mycosis. Widespread fungal infections with complicated and variable clinical manifestations, such as Candida auris infection resistant to several antifungal medicines, Covid-19 associated with Trichoderma, and terbinafine resistant dermatophytosis in India, are among the most serious disorders. \r\nInappropriate local or systemic use of glucocorticoids, as well as their immunosuppressive effects, may lead to changes in fungal infection spectrum and clinical characteristics. Hematogenous candidiasis is a worrisome issue that affects people all over the world, particularly ICU patients. CARD9 deficiency and fungal infection have been major issues in recent years. Invasive aspergillosis is associated with a significant death rate. 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International Union of Microbiological Societies (IUMS) Fellow, and International Emerging Infectious Diseases (IEID) Fellow, Centers for Diseases Control and Prevention (CDC), Atlanta, USA. Diploma of Dermatological Scientist, Japanese Society for Investigative Dermatology. Ph.D. of Juntendo University, Japan. Bachelor’s and Master’s degree, Medicine, West China University of Medical Sciences. Chair of Sichuan Medical Association Dermatology Committee. General Secretary of The 19th Annual Meeting of Chinese Society of Dermatology and the Asia Pacific Society for Medical Mycology (2013). In charge of the Annual Medical Mycology Course over 20-years authorized by National Continue Medical Education Committee of China. Member of the board of directors of the Asia-Pacific Society for Medical Mycology (APSMM). Associate editor of Mycopathologia. Vice-chief of the editorial board of Chinses Journal of Mycology, China. 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The considerable development of technology, including the computing power of computers, is also conducive to the development of bioinformatics, including personalized medicine. In an era of rapidly growing data volumes and ever lower costs of generating, storing and computing data, personalized medicine holds great promises. Modern computational methods used as bioinformatics tools can integrate multi-scale, multi-modal and longitudinal patient data to create even more effective and safer therapy and disease prevention methods. Main aspects of the topic are: Applying bioinformatics in drug discovery and development; Bioinformatics in clinical diagnostics (genetic variants that act as markers for a condition or a disease); Blockchain and Artificial Intelligence/Machine Learning in personalized medicine; Customize disease-prevention strategies in personalized medicine; Big data analysis in personalized medicine; Translating stratification algorithms into clinical practice of personalized medicine.",annualVolume:11403,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/7.jpg",editor:{id:"351533",title:"Dr.",name:"Slawomir",middleName:null,surname:"Wilczynski",fullName:"Slawomir Wilczynski",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y000035U1loQAC/Profile_Picture_1630074514792",institutionString:null,institution:{name:"Medical University of Silesia",institutionURL:null,country:{name:"Poland"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"5886",title:"Dr.",name:"Alexandros",middleName:"T.",surname:"Tzallas",fullName:"Alexandros Tzallas",profilePictureURL:"https://mts.intechopen.com/storage/users/5886/images/system/5886.png",institutionString:"University of Ioannina, Greece & Imperial College London",institution:{name:"University of Ioannina",institutionURL:null,country:{name:"Greece"}}},{id:"257388",title:"Distinguished Prof.",name:"Lulu",middleName:null,surname:"Wang",fullName:"Lulu Wang",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRX6kQAG/Profile_Picture_1630329584194",institutionString:"Shenzhen Technology University",institution:{name:"Shenzhen Technology University",institutionURL:null,country:{name:"China"}}},{id:"225387",title:"Prof.",name:"Reda R.",middleName:"R.",surname:"Gharieb",fullName:"Reda R. Gharieb",profilePictureURL:"https://mts.intechopen.com/storage/users/225387/images/system/225387.jpg",institutionString:"Assiut University",institution:{name:"Assiut University",institutionURL:null,country:{name:"Egypt"}}}]},{id:"8",title:"Bioinspired Technology and Biomechanics",keywords:"Bioinspired Systems, Biomechanics, Assistive Technology, Rehabilitation",scope:'Bioinspired technologies take advantage of understanding the actual biological system to provide solutions to problems in several areas. Recently, bioinspired systems have been successfully employing biomechanics to develop and improve assistive technology and rehabilitation devices. The research topic "Bioinspired Technology and Biomechanics" welcomes studies reporting recent advances in bioinspired technologies that contribute to individuals\' health, inclusion, and rehabilitation. Possible contributions can address (but are not limited to) the following research topics: Bioinspired design and control of exoskeletons, orthoses, and prostheses; Experimental evaluation of the effect of assistive devices (e.g., influence on gait, balance, and neuromuscular system); Bioinspired technologies for rehabilitation, including clinical studies reporting evaluations; Application of neuromuscular and biomechanical models to the development of bioinspired technology.',annualVolume:11404,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/8.jpg",editor:{id:"144937",title:"Prof.",name:"Adriano",middleName:"De Oliveira",surname:"Andrade",fullName:"Adriano Andrade",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRC8QQAW/Profile_Picture_1625219101815",institutionString:null,institution:{name:"Federal University of Uberlândia",institutionURL:null,country:{name:"Brazil"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"49517",title:"Prof.",name:"Hitoshi",middleName:null,surname:"Tsunashima",fullName:"Hitoshi Tsunashima",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYTP4QAO/Profile_Picture_1625819726528",institutionString:null,institution:{name:"Nihon University",institutionURL:null,country:{name:"Japan"}}},{id:"425354",title:"Dr.",name:"Marcus",middleName:"Fraga",surname:"Vieira",fullName:"Marcus Vieira",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y00003BJSgIQAX/Profile_Picture_1627904687309",institutionString:null,institution:{name:"Universidade Federal de Goiás",institutionURL:null,country:{name:"Brazil"}}},{id:"196746",title:"Dr.",name:"Ramana",middleName:null,surname:"Vinjamuri",fullName:"Ramana Vinjamuri",profilePictureURL:"https://mts.intechopen.com/storage/users/196746/images/system/196746.jpeg",institutionString:"University of Maryland, Baltimore County",institution:{name:"University of Maryland, Baltimore County",institutionURL:null,country:{name:"United States of America"}}}]},{id:"9",title:"Biotechnology - Biosensors, Biomaterials and Tissue Engineering",keywords:"Biotechnology, Biosensors, Biomaterials, Tissue Engineering",scope:"The Biotechnology - Biosensors, Biomaterials and Tissue Engineering topic within the Biomedical Engineering Series aims to rapidly publish contributions on all aspects of biotechnology, biosensors, biomaterial and tissue engineering. We encourage the submission of manuscripts that provide novel and mechanistic insights that report significant advances in the fields. Topics can include but are not limited to: Biotechnology such as biotechnological products and process engineering; Biotechnologically relevant enzymes and proteins; Bioenergy and biofuels; Applied genetics and molecular biotechnology; Genomics, transcriptomics, proteomics; Applied microbial and cell physiology; Environmental biotechnology; Methods and protocols. Moreover, topics in biosensor technology, like sensors that incorporate enzymes, antibodies, nucleic acids, whole cells, tissues and organelles, and other biological or biologically inspired components will be considered, and topics exploring transducers, including those based on electrochemical and optical piezoelectric, thermal, magnetic, and micromechanical elements. Chapters exploring biomaterial approaches such as polymer synthesis and characterization, drug and gene vector design, biocompatibility, immunology and toxicology, and self-assembly at the nanoscale, are welcome. Finally, the tissue engineering subcategory will support topics such as the fundamentals of stem cells and progenitor cells and their proliferation, differentiation, bioreactors for three-dimensional culture and studies of phenotypic changes, stem and progenitor cells, both short and long term, ex vivo and in vivo implantation both in preclinical models and also in clinical trials.",annualVolume:11405,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/9.jpg",editor:{id:"126286",title:"Dr.",name:"Luis",middleName:"Jesús",surname:"Villarreal-Gómez",fullName:"Luis Villarreal-Gómez",profilePictureURL:"https://mts.intechopen.com/storage/users/126286/images/system/126286.jpg",institutionString:null,institution:{name:"Autonomous University of Baja California",institutionURL:null,country:{name:"Mexico"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"35539",title:"Dr.",name:"Cecilia",middleName:null,surname:"Cristea",fullName:"Cecilia Cristea",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYQ65QAG/Profile_Picture_1621007741527",institutionString:null,institution:{name:"Iuliu Hațieganu University of Medicine and Pharmacy",institutionURL:null,country:{name:"Romania"}}},{id:"40735",title:"Dr.",name:"Gil",middleName:"Alberto Batista",surname:"Gonçalves",fullName:"Gil Gonçalves",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002aYRLGQA4/Profile_Picture_1628492612759",institutionString:null,institution:{name:"University of Aveiro",institutionURL:null,country:{name:"Portugal"}}},{id:"211725",title:"Associate Prof.",name:"Johann F.",middleName:null,surname:"Osma",fullName:"Johann F. 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