Simulation performance assessment for the floor structure using several control gains and walking excitation. (1) Maximum Transient Vibration value defined as the maximum value of 1s running RMS acceleration. (2) Cumulative Vibration Dose Value
\r\n\t*the fundamentals and experimental methods of acoustic cavitation
\r\n\t*organic / inorganic synthesis,
\r\n\t*nanomaterials (encapsulated nanoparticles, metal oxide nanoparticles, nanopowders, nanocollides, nanotubes, nanorods, nanowires, nanofilms, nanoplatelets, nanosheets, nanoribbons, nanobelts, nanoplates, nanodots, nanoalloys, nanodiscs, nanorings, nanotripods nanobricks, nanonails, nanoarrows, nanospheres),
Advances in structural technologies, including construction materials and design technologies, have enabled the design of light and slender structures, which have increased susceptibility to human-induced vibration. This is compounded by the trend toward open-plan structures with fewer non-structural elements, which have less inherent damping. Examples of notable vibrations under human-induced excitations have been reported in floors, footbridges and grandstands, amongst other structures (Bachmann, 1992; Bachmann, 2002; Hanagan et al., 2003a). Such vibrations can cause a serviceability problem in terms of disturbing the users, but they rarely affect the fatigue behaviour or safety of structures.
Solutions to overcome human-induced vibration serviceability problems might be: (i) designing in order to avoid natural frequencies into the habitual pacing rate of walking, running or dancing, (ii) stiffening the structure in the appropriate direction resulting in significant design modifications, (iii) increasing the weight of the structure to reduce the human influence being also necessary a proportional increase of stiffness and (iv) increasing the damping of the structure by adding vibration absorber devices. The addition of these devices is usually the easiest way of improving the vibration performance. Traditionally, passive vibration absorbers, such as tuned mass dampers (TMDs) (Setareh & Hanson, 1992; Caetano et al., 2010), tuned liquid dampers (Reiterer & Ziegler, 2006) or visco-elastic dampers, etc., have been employed. However, the performance of passive devices is often of limited effectiveness if they have to deal with small vibration amplitude (such as those produced by human loading) or if vibration reduction over several vibration modes is required since they have to be tuned to a single mode. Semi-active devices, such semi-active TMDs, have been found to be more robust in case of detuning due to structural changes, but they exhibit only slightly improved performance over passive TMDs and they still have the fundamental problem that they are tuned to a single problematic mode (Setareh, 2002; Occhiuzzi et al., 2008). In these cases, an active vibration control (AVC) system might be more effective and then, an alternative to traditional passive devices (Hanagan et al., 2003b). A state-of-the-art review of technologies (passive, semi-active and active) for mitigation of human-induced vibration can be found in (Nyawako & Reynolds, 2007). Furthermore, techniques to cancel floor vibrations (especially passive and semi-active techniques) are reviewed in (Ebrahimpour & Sack, 2005) and the usual adopted solutions to cancel footbridge vibrations can be found in (FIB, 2005).
An AVC system based on direct velocity feedback control (DVFC) with saturation has been studied analytically and implemented experimentally for the control of human-induced vibrations via an active mass damper (AMD) (also known as inertial actuator or proof-mass actuator) on a floor structure (Hanagan & Murray, 1997) and on a footbridge (Moutinho et al., 2010). This actuator generates inertial forces in the structure without need for a fixed reference. The velocity output, which is obtained by an integrator circuit applied to the measured acceleration response, is multiplied by a constant gain and feeds back to a collocated force actuator. The term collocated means that the actuator and sensor are located physically at the same point on the structure. The merits of this method are its robustness to spillover effects due to high-order unmodelled dynamics and that it is unconditionally stable in the absence of actuator and sensor (integrator circuit) dynamics (Balas, 1979). Nonetheless, when such dynamics are considered, the stability for high gains is no longer guaranteed and the system can exhibit limit cycle behaviour, which is not desirable since it could result in dramatic effects on the system performance and its components (Díaz & Reynolds, 2010a). Then, DVFC with saturation is not such a desirable solution. Generally, the actuator and sensor dynamics influence the system dynamics and have to be considered in the design process of the AVC system. If the interaction between sensor/actuator and structure dynamics is not taken into account, the AVC system might exhibit poor stability margins, be sensitive to parameter uncertainties and be ineffective. A control strategy based on a phase-lag compensator applied to the structure acceleration (Díaz & Reynolds, 2010b), which is usually the actual magnitude measured, can alleviated such problems. This compensator accounts for the interaction between the structure and the actuator and sensor dynamics in such a way that the closed-loop system shows desirable properties. Such properties are high damping for the fundamental vibration mode of the structure and high stability margins. Both properties lead to a closed-loop system robust with respect to stability and performance (Preumont, 1997). This control law is completed by: (i) a high-pass filter, applied to the output of the phase-lag compensator, designed to avoid actuator stroke saturation due to low-frequency components and (ii) a saturation nonlinearity applied to the control signal to avoid actuator force overloading at any frequency. This methodology will be referred as to compensated acceleration feedback control (CAFC) from this point onwards.
This chapter presents the practical implementation of an AMD to cancel excessive vertical vibrations on an in-service office floor and on an in-service footbridge. The AMD consists of a commercial electrodynamic inertial actuator controlled via CAFC. The remainder of this chapter is organised as follows. The general control strategy together with the structure and actuator dynamic model are described in Section 2. The control design procedure is described in Section 3. Section 4 deals with the experimental implementation of the AVC system on an in-service open-plan office floor whereas Section 5 deals with the implementation on an in-service footbridge. Both sections contain the system dynamic models, the design of CAFC and results to assess the design. Finally, some conclusions are given in Section 6.
The main components of the general control strategy adopted in this work are shown in Fig. 1. The output of the system is the structural acceleration since this is usually the most convenient quantity to measure. Because it is rarely possible to measure the system state and due to simplicity reasons, direct output measurement feedback control might be preferable rather than state-space feedback in practical problems (Chung & Jin, 1998). In this Fig., GA is the transfer function of the actuator, G is of the structure, CD is of the direct compensator and CF is of the feedback compensator. The direct one is merely a phase-lead compensator (high-pass property) designed to avoid actuator stroke saturation for low-frequency components. It is notable that its influence on the global stability will be small since only a local phase-lead is introduced. The feedback one is a phase-lag compensator designed to increase the closed-loop system stability and to make the system more amenable to the introduction of significant damping by a closed-loop control. The control law is completed by a nonlinear element f that is assumed to be a saturation nonlinearity to account for actuator force overloading.
If the collocated case between the acceleration (output) and the force (input) is considered and using the modal analysis approach, the transfer function of the structure dynamics can be represented as an infinitive sum of second-order systems as follows (Preumont, 1997)
where, is the frequency, , and are the inverse of the modal mass, damping ratio and natural frequency associated to the i-th mode, respectively. For practical application, N vibration modes are considered in the frequency bandwidth of interest. The transfer function G (1) is thus approximated by a truncated one as follows
The actuator consists of a reaction (moving) mass attached to a current-carrying coil moving in a magnetic field created by an array of permanent magnets. The linear behaviour of a proof-mass actuator can be closely described as a linear third-order model (Reynolds et al., 2009). That is, a low-pass element is added to a linear second-order system in order to account for the low-pass property exhibited by these actuators. The cut-off frequency of this element is not always out of the frequency bandwidth of interest since it is approximately 10 Hz (APS). Such a low-pass behaviour might affect importantly the global stability of the AVC system. Thus, the actuator is proposed to be modelled by
where, and and are, respectively, the damping ratio and natural frequency which take into consideration the suspension system and internal damping. The pole at provides the low-pass property.
The purpose of this section is to show a procedure to design the compensators CD and CF (see Fig. 1). The design of CD is undertaken in the frequency domain and the design of CF is carried out through the root locus technique. The root locus maps the complex linear system roots of the closed-loop transfer function for control gains from zero (open-loop) to infinity (Bolton, 1998). In the design of CF, it is assumed that the natural frequency of the actuator (see Eq. (3)) is below the first natural frequency of the structure (see Eq. (2)) (Hanagan, 2005).
The transfer function between the inertial mass displacement and input voltage to the actuator can be considered as follows
with mA being the mass value of the inertial mass. Fig. 2a shows an example of magnitude of Gd. The inertial mass displacement at low frequencies should be limited due to stroke saturation. A transfer function with the following magnitude is defined
in which d is the maximum allowable stroke for harmonic input per unit voltage and is the higher frequency that fulfils. A high-pass compensator of the form
with, , , and and being, respectively, the lower and upper value of the frequency range that is considered in the design. The lower frequency must be selected in such a way that the actuator resonance is sufficiently included and the upper frequency must be chosen so that the structure dynamics that are prone to be excited are included. Parameters\n\t\t\t\t\t and of the compensator are obtained by minimising the error function (7)
with, , , and and being, respectively, the maximum considered value of and for the optimisation problem (8). Note that and are delimited by the low-pass property of the actuator in order to minimise the influence of CD on the global stability properties. By and large, the objective is to fit to d for and not to affect the dynamics for (see Fig. 2a). The result is a high-pass compensator that introduces dynamics mainly in the frequency range in such a way that the global stability is not compromised.
To illustrate the selection of the form of the compensator CF, the root locus map (s-plane) for four different cases is shown in Fig. 3. A realistic structure is assumed with two significant vibration modes. The modal mass and damping ratio for both modes are assumed to be 20 tonnes and 0.03, respectively. The four cases are: a) direct acceleration feedback control (DAFC) considering two vibration modes at 4 and 10 Hz, respectively; b) DVFC for the same structure as in a); c) DAFC considering two vibration modes at 7 and 10 Hz, respectively; and d) DVFC for the same structure as in c). The actuator dynamics (Eq. (3)) is represented by a pair of high-damped poles, two zeros at the origin and a real pole and the structure is represented by two zeros at the origin and interlacing low-damped poles and zeros. It is clearly shown that the resulting root locus has non-collocated system features due to the influence of the actuator dynamics on the structure dynamics. That is, when the actuator dynamics are considered, the interlacing pole-zero pattern exhibited by collocated systems is
no longer accomplished. On one hand, it is observed that for a structure with a fundamental frequency of 4 Hz, direct output feedback (DAFC since the actual measurement is the acceleration) will provide very small relative stability (the distance of the poles to the imaginary axis in the s-plane) and low damping (Bolton, 1998). However, the inclusion of an integrator circuit (a pole at the origin for an ideal integrator), which results in DVFC, improves substantially such properties. On the other hand, for a structure with a higher fundamental frequency (7 Hz), DAFC provides much better features than DVFC.
Fig. 3 shows the fact that DVFC might not be a good solution and supports the use of CAFC. It is applied the following phase-lag compensator to the measured acceleration
If, the control scheme will be DAFC since. If, which means that the zero of the compensator does not affect the dominant system dynamics, the control scheme will then be considered DVFC. Parameter has to be chosen according to the closed-loop poles corresponding to the fundamental frequency of the structure in order to: 1) improve substantially their relative stability, 2) decrease their angles with respect to the negative real axis to allow increasing damping, and 3) increase the distance to the origin to allow increasing natural frequency. Note that increasing values both of the frequency and the damping result in decreasing the settling time of the corresponding dynamics (Bolton, 1998).
The possible values of that provide the aforementioned features can be bound through the departure angle at zero gain of the locus corresponding to the fundamental structure vibration mode. This angle must point to negative values of the real axis. To obtain this angle, the argument equation of the closed-loop characteristic equation is used. That is, any point s1 of a specific trajectory verifies the following equation
in which nz is the number of zeros, np is the number of poles and and are the angles of vectors drawn from the zeros and poles, respectively, to point s1. The departure angle can be determined by letting s1 be a point very close to one of the poles of the fundamental structure vibration mode. As an example, the dominant dynamics are considered without the direct compensator. Fig. 4 shows the map of zeros and poles under the aforementioned conditions. Eq. (10) can be written as follows
If it is considered that the damping of the fundamental vibration mode is, the following assumptions can be done: and. Therefore, Eq. (11) can be rewritten as
Then, by imposing a minimum and a maximum value of the departure angle of the fundamental structure vibration mode, a couple of values of can be obtained
in which it is assumed. Therefore, the variation interval of is derived as follows
and using Eq. (14), the corresponding variation interval of is determined. The final value of must be chosen so that the attractor properties of the zero are focussed on the fundamental vibration mode.
Stability is the primary concern in any active control system applied to civil engineering structures, mainly due to safety and serviceability reasons. The control scheme of Fig. 1, assuming that the nonlinear element f is a saturation nonlinearity, is analysed in this section. The nonlinear element can be written as
where Kc is the control gain and Vs is the maximum allowable control voltage to the actuator (saturation level). The saturation nonlinearity is introduced to avoid actuator force saturation and to keep the system safe under any excitation and independently of selection of control parameters. The stability can be studied using the Describing Function (DF) tool in its basic form (Slotine & Li, 1991). Firstly, the total transfer function of the linear part (Eqs. (2), (3), (6) and (9)) is obtained (see Fig.1)
Then, from the root locus of GT, the limit gain for which the closed-loop system becomes unstable is derived. This is the minimum value of the control gain Kc (see Eq. (17)) for which at least one of the loci intersects the imaginary axis.
Secondly, the DF, denoted by, for the nonlinear element is obtained. The DF is the ratio between the fundamental component of the Fourier series of the nonlinear element output and a sinusoidal input given by. If the nonlinearity is hard, odd and single-valued (the case of saturation nonlinearity), the DF depends only on the input amplitude, i.e., it is a real function. The DF for a saturation nonlinearity is (Slotine & Li, 1991)
with (see Eq. (17)). The normalised DF (19) is plotted in Fig. 5a as a function of. If the input amplitude is in the linear range, is constant and equal to the control gain. then decreases as the input amplitude increases when. That is, saturation does not occur for small signals and it reduces the ratio of the output to input as the input increases.
Thirdly, the extended Nyquist criterion using the DF is applied
Each solution of Eq. (20) predicts a limit cycle behaviour (self-sustained periodic undesirable vibration). The total transfer function will intersect the real axis at. With regards to the plot of, it will start at and go to as A increases. Depending on the value of, both plots and can intersect. Fig. 5b illustrates this fact. The conclusion is that: if, the system is asymptotically stable and goes to zero vibration (no intersection); otherwise, a limit cycle is predicted (intersection). Such a limit cycle is deduced to be stable by using the limit cycle stability criterion (Slotine & Li, 1991; Díaz & Reynolds, 2010a). The properties of the limit cycle, frequency and amplitude, can be obtained by Eq. (20) particularised to the intersection point.
The design process of the control scheme represented in Fig. 1 can be summarised in the following steps:
Step 1: Identify the actuator GA and structure dynamics G.
Step 2: Design the direct compensator (phase-lead) CD accounting for the actuator stroke saturation. This design is carried out following the procedure described in Subsection 3.1.
Step 3: Design the feedback (phase-lag) compensator CF to increase the damping and robustness with respect to stability and performance of the closed-loop system by following Subsection 3.2.
Step 4: Design the nonlinear element f according to stability and performance. If f is a saturation nonlinearity, take a saturation value to avoid actuator force overloading and select a suitable gain Kc using the root locus method.
This Section presents the design and practical implementation of an AVC system based on the procedure presented in Section 3 on an in-service open-plan office floor sited in the North of England.
The test structure is a composite steel-concrete floor in a steel frame office building. A plan of the floor is shown in Fig. 6a, in which the measurement points used for the experimental modal analysis (EMA) are indicated. Columns are located along the two sides of the building (without point numbers) and along the centreline (18-27-end), at every other test point (TP) location (i.e, 18, 20, 22, etc.). Fig 6b shows a photograph from TP 44 towards TP 28 and Fig. 6c shows a photograph from TP 12 towards TP 01. The EMA of this structure is explained in detail in (Reynolds et al., 2009). The floor is considered by its occupants to be quite lively, but not sufficiently lively to attract complaints. Special attention is paid to TP 04 (see Fig. 6a) and its surroundings because it is perceived to be a particularly lively location on the floor. Because the vibration perception is particularly acute at this point, this is the candidate for the installation of the AVC system.
A multi-input multi-output modal testing is carried out with four excitation points placed at TPs 04, 07, 31 and 36 and responses measured at all TPs. The artificial excitation is supplied by APS Dynamics Model 400 electrodynamic shakers (Fig. 7b) and responses are measured by QA750 force-balance accelerometers (Fig. 7c). Fig 7a shows a photograph of the multishaker modal testing carried out. Fig. 8 shows the magnitudes of the point accelerance FRFs acquired. Interestingly, the highest peak occurs at TP 04 at approximately 6.4 Hz, which is the point on the structure where the response has been subjectively assessed to be highest. Parameter estimation is carried out using the multiple reference orthogonal polynomial algorithm already implemented in ME’scope suite of software. Fig. 9 shows the estimated vibration modes which are dominant at TP 04.
The AVC system is placed at TP 04. The floor dynamics at the AVC location (Eq. (2)) and the actuator dynamics (Eq. (3)) are identified. Using the modal parameters obtained from the EMA, the transfer function of the floor is modelled considering three vibration modes in the frequency range of 0–20 Hz
The inertial actuator is an APS Dynamics Model 400 electrodynamic shaker (operated in inertial mode and driven using voltage mode) with an inertial mass of (APS Manual). The actuator model is obtained to be
The natural frequency of the actuator is estimated as 1.80 Hz and the pole that provides the low pass property is estimated to be (Eq. (3)).
Compensators CD and CF are obtained following Section 3. Firstly, CD is obtained. From (22), the transfer function Gd (Eq. (4)) is derived. By assuming a value of, which is appropriate considering the actual stroke limit of the actuator is 0.075 m, its magnitude (Eq. (5)) is obtained with. The compensator parameters are thus derived from the optimisation problem (8) in which it is assumed, and. The control parameters are then found to be and.
Secondly, the feedback compensator CF (Eq. (9)) is obtained. Taking into account the dominant dynamics: GA, CD and the fundamental floor vibration mode of (21) (the first one of the three considered mode), and restricting the departure angle of the locus corresponding to the structure vibration mode as (see Fig. 4), then the angle corresponding to the zero of the compensator can be bounded. It is obtained and consequently using Eq. (14). A value of is chosen since it must be higher than the inferior limit but it should not be so high that the attractor effect of the zero is focussed on the fundamental vibration mode. The root locus technique is used here. The root locus of GT (Eq. (18)) for CAFC is plotted in Fig. 10. It can be observed that the linear system might be critically damped for the fundamental floor vibration mode.
Finally, the nonlinear element is chosen as a saturation nonlinearity (17) with, which is a convenient value to avoid actuator force overloading at any frequency of the excitation. Therefore, the stability is guaranteed just by taking a safe control gain. The limit gain is predicted to be. Values of damping of the actuator poles smaller than 0.30 are not recommended (Hanagan, 2005). This damping is reached for.
A digital computer is used for the on-line calculation of the control signal V. The system output is sampled with a period and the control signal is calculated once every sampling period. Then, the discrete-time control signal is converted into a zero-order-hold continuous-time signal. Likewise, the continuous transfer functions of the compensators are converted to discrete transfer function using the zero-order-hold approximation. Note that the sampled period used is sufficiently small to not consider the delay introduced by the digital implementation of the control scheme.
The AVC system is assessed firstly by carrying out several simulations using different values of the control gain Kc. MATLAB/Simulink is used for this purpose. The control scheme shown in Fig. 1 is simulated using the transfer function models of the compensators given by Eqs. (6) and (9) with the parameters obtained in Section 4.3 and Eqs. (21) and (22) obtained from FRF identifications. The control scheme is perturbed by a real walking excitation obtained from an instrumented treadmill (Brownjohn et al., 2004) (in Fig. 1). Table 1 shows the results obtained. Two different pacing frequencies (1.58 and 2.12 Hz) are used in such a way that the first floor vibration mode might be excited by the third or the fourth harmonic. The results are compared in terms of the maximum transient vibration value (MTVV) calculated from the 1 s running RMS acceleration and from the vibration dose value (VDV) obtained from the total period of the excitation (BS 6472, 2008). The BS 6841 Wb weighted acceleration is used for both measures (BS 6841, 1987). The results predicted that the AVC are quite insensitive to the gain value. The reduction in vibration is approximately 60 % for slow walking (1.58 Hz) and 53 % for fast walking (2.12 Hz) in terms of MTVV. The results in terms of the VDV provide similar reductions as for the MTVV.
|Control gain (V/(m/s2))||Uncontrolled||5||10||15||20|
|Walking at 1.58 Hz|
|Reduction MTVV (%)||59||62||62||61|
|Reduction VDV (%)||55||58||58||57|
|Walking at 2.12 Hz|
|Reduction MTVV (%)||53||55||53||52|
|Reduction VDV (%)||54||56||55||55|
Actual walking tests are carried out on the test structure using the same walking excitation frequencies as in the simulations. The walking path consists of walking from TP 01 to TP 09 and then back from TP 09 to TP 01 (see Fig. 6). A gain of is found to give good performance so that is used in the experiments. Fig. 11 shows BS 6841 Wb weighted response time histories (including the 1s RMS and the cumulative VDV), uncontrolled and controlled, for a pacing frequency of 1.58 Hz, which is controlled using a metronome set to 95 beats per minute (bpm). The MTVV is reduced from to, a reduction of 68 %, and the VDV is reduced from to, a reduction of 62 %. The same test is carried out for a pacing frequency of 2.12 Hz (127 bpm). The achieved reduction in terms of the MTVV is now 52 %, from to, and in terms of the VDV is 51 %, from to. The experimental reductions agreed very well with the numerical predictions (see Table 1).
Continuous whole-day monitoring has been carried out to assess the vibration reduction achieved by the AVC system. The acceleration is measured from 6:00 am to 6:00 pm during four working days, two without and two with the AVC system. The R-factor is used to quantify the vibration reduction. This factor is defined as the ratio between the 1 s running RMS of the BS 6841 Wb weighted acceleration response and 0.005 m/s2 (Wyatt, 1989). Fig. 12 shows the percentage of time during which the R-factor is over 1, 2, 3, 4 and 5. The values
shown in the Fig. are the mean values between the two corresponding days. It is observed that the time for which the R-factor is over 1 is reduced by 60 % and the time for which it is over 4 is significantly reduced by over 97 %. Note that the second reduction is very important since an R-factor of 4 is a commonly used vibration limit for a high quality office floor (Pavic & Willford, 2005). Hence, these results clearly illustrate the effectiveness of the AVC system designed. In addition, the cumulative VDV is also calculated for the same exposure to vibration and using the Wb weighted acceleration. The VDV obtained when the AVC system is disconnected is whereas such a value is when the system is engaged. The reduction achieved is almost 40 %. Note that the VDV is much more strongly influenced by vibration magnitude than duration (BS 6472, 2008). This fact results in less vibration reduction in terms of the VDV than using the MTVV.
This Section presents the design and practical implementation of an AVC system based on the procedure presented in Section 3 on an in-service footbridge sited in Valladolid (Spain).
The test structure, sited in Valladolid (Spain), is a footbridge that creates a pedestrian link over The Pisuerga River between the Science Museum and the city centre (see Fig. 13). This bridge, built in 2004, is a 234 m truss structure composed of four spans: three made of tubular steel beams and one made of white concrete, all of them with a timber walkway. The main span (Span 3 in Fig. 1), post-tensioning by two external cable systems (transversal and longitudinal), is 111 m, the second span (Span 2 from this point onwards) is 51 m and the other two spans are shorter and stiffer (Gómez, 2004). The external cable systems of Span 3 has both aesthetical reasons (the original design by the architect José Rafael Moneo was based on the form of a fish basket) and structural reasons (making Span 3 stiffer).
Because of its slenderness, this footbridge, especially Span 2, represents a typical lightweight structure sensitive to dynamic excitations produced by pedestrians. Annoying levels of vibration are sometime perceived in Span 2. Special attention is paid to the point of maximum amplitude of the first bending mode (close to mid-span) since the vibration perception is acute at this point, particularly when runners cross the bridge. Therefore, it is decided to study the dynamic properties of this span and implement the AVC system at that point.
The operational modal analysis of Span 2 is carried out in order to obtain the natural frequencies, damping ratios and modal shapes of the lower vibration modes. The analysis is carried out with five roving and two reference accelerometers. Preliminary spectral analyses and time history recordings indicates that the vertical vibration is considerably higher than the horizontal one, thus, only vertical response measurements are performed. A measurement grid of 3 longitudinal lines with 9 equidistant test points is considered, resulting in 27 test points. Five setups with an acquisition time of 720 seconds and a sampling frequency of 100 Hz are recorded. Thus, it is expected to successfully identify vibration modes up to 30 Hz. The modal parameter estimation is carried out using the ARTeMIS suite of software. In particular, frequency domain methods (Frequency domain decomposition-FDD, enhanced frequency domain decomposition-EFDD and curve-fit frequency domain decomposition-CFDD) are used. Table 2 shows the modal parameters estimated through the modal analysis for the first four vibration modes. Fig. 14 shows the corresponding estimated modal shapes.
|Mode 1||Mode 2||Mode 3||Mode 4|
|Damping ratio (%)|
|Damping ratio (%)||0.7221||0.4167||0.6571||0.5528|
|Damping ratio (%)||0.7984||0.2599||0.4319||0.3869|
The FRF between the structure acceleration and the input force is obtained at the middle of the transversal steel beam sited closest to the point of maximum value of the first vibration mode (close to mid-span). A chirp signal with frequency content between 1 and 15 Hz is used to excite the first vibration modes. The force is generated by an APS Dynamics Model 400 electrodynamic (as was used for the floor) and the structure acceleration is measured by a piezoelectric accelerometer (as those used for the modal analysis). The force induced by the shaker is estimated by measuring the acceleration of the inertial mass and multiplying this by the magnitude of the inertial mass (30.4 kg). Thus, the structure dynamics for the collocated case between the acceleration (output) and the force (input) can be identified from model (2) as follows
The vibration modes at 6.3 and 7.4 Hz (see Fig. 14) are not clearly observed and they are not included into this model. The same shaker that is used to obtain the FRF for the structure is used as inertial actuator. The transfer function between the output force and the input voltage is the one given by Eq. (22).
The design process shown in Section 3 is now followed. The direct compensator of the form of (6) is assumed. Again, a maximum stroke for harmonic excitation of d = 0.05 m is considered in the design. The compensator parameters are obtained from the optimisation problem (8) using the parameter used in Subsection 4.3. The controller parameters are found to be and. These parameters are selected in such a way that the likelihood of stroke saturation is reduced significantly. The stroke saturation leads to collisions of the inertial mass with its stroke limits, imparting highly undesirable shocks to the structure and possibly causing damage to the actuator.
Once the direct compensator is designed, the feedback one (9) is designed considering the dynamics of the actuator, structure and the direct compensator dynamics. As in Subsection 4.3, the departure angle of the locus corresponding to the structure vibration mode is restricted to (see Fig. 4). It is obtained. A value of is finally chosen. The root locus technique is now used. The root locus of the total transfer function of the linear part (18) is plotted in Fig. 15 (only the dominant dynamics are shown). It is observed that a couple of branches in the root locus corresponding to the actuator dynamics go to the right-half plane provoking unstable behaviour in the actuator. The gain for which the control system is unstable is the limit gain. Finally, a gain of is chosen. The saturation level is set to.
Once both compensators and the control parameters are selected, simulations are carried out in order to assess the AVC performance. MATLAB/Simulink is again used for this purpose. Table 3 shows controlled acceleration response for walking and running excitation. Moreover, the AMD displacement estimation is included.
|Uncontrolled (m/s2)||Controlled (m/s2)||Reduction (%)||Mass displacement (m)|
|Walking at 1.75 Hz||0.39||0.04||89||0.034|
|Running at 3.50 Hz||6.16||3.75||40||0.022|
Walking and running tests are carried out to assess the efficacy of the AVC system. The walking tests consist of walking at 1.75 Hz such that the first vibration mode of the structure (3.5 Hz) could be excited by the second harmonic of walking. A frequency of 3.5 Hz is used for the running tests so that the structure is excited by the first harmonic of running. The walking/running tests consisted of walking/running from one end of Span 2 to the other and back again. The pacing frequency is controlled using a metronome set to 105 beats per minute (bpm) for 1.75 Hz and to 210 bpm for 3.5 Hz. Each test is repeated three times.
|Walking at 1.75 Hz|
|Peak acceleration (m/s2)||0.41||0.16||70|
|Running at 3.50 Hz|
|Peak acceleration (m/s2)||3.34||1.19||64|
The results are compared by means of the maximum peak acceleration and the MTVV computed from the 1 s running RMS acceleration. Table 4 shows the result obtained for the uncontrolled and controlled case. It is observed that the AMD designed (with a moving mass of 30 kg) performs well for both excitations, achieving reductions of approximately 70 %. Fig. 16 shows the response time histories (including the 1 s RMS) uncontrolled and controlled for a walking test. Fig. 17 shows the same plots for a running test.
The active cancellation of human-induced vibrations has been considered in this chapter. Even velocity feedback has been used previously for controlling human-induced vibrations, it has been shown that this is not a desirable solution when the actuator dynamics influence the structure dynamics. Instead of using velocity feedback, here, it is used a control scheme base on the feedback of the acceleration (which is the actual measured output) and the use of a first-order compensator (phase-lag network) conveniently designed in order to achieve significant relative stability and damping. Note that the compensator could be equivalent to an integrator circuit leading to velocity feedback, depending on the interaction between actuator and structure dynamics. Moreover, the control scheme is completed by a phase-lead network to avoid stroke saturation due to low-frequency components of excitations and a nonlinear element to account for actuator overloading. An AVC system based on this control scheme and using a commercial inertial actuator has been tested on two in-service structures, an office floor and a footbridge.
The floor structure has a vibration mode at 6.4 Hz which is the most likely to be excited. This mode has a damping ratio of 3% and a modal mass of approximately 20 tonnes. Reductions of approximately 60 % have been observed in MTVV and cumulative VDV for controlled walking tests. For in-service whole-day monitoring, the amount of time that an R-factor of 4 is exceeded, which is a commonly used vibration limit for high quality office floor, is reduced by over 97 %. The footbridge has a vibration mode at 3.5 Hz which is the most likely to be excited. This mode has a damping ratio of 0.7 % and a modal mass of approximately 18 tonnes. Reductions close to 70 % in term of the MTVV has been achieved for walking and running tests.
It has been shown that AVC could be a realistic and reasonable solution for flexible lightweight civil engineering structures such as light-weight floor structure or lively footbridges. In these cases, in which low control forces are required (as compared with other civil engineering applications such as high-rise buildings or long-span bridges), electrical actuators can be employed. These actuators present advantages with respect to hydraulic ones such as lower cost, maintenance and level of noise. However, AVC systems for human-induced vibrations needs much further research and development to jump into building and construction technologies considered by designers. With respect to passive systems, such as TMDs, cost is still the mayor disadvantage. However, it is expected that this technology will become less expensive and more reasonable in the near future. Research projects involving the development of new affordable and compact actuators for human-induced vibration control are currently on the go (Research Grant EP/H009825/1, 2010).
The author would like to acknowledge the financial support of Universidad de Castilla-La Mancha (PL20112170) and Junta de Comunidades de Castilla-La Mancha (PPII11-0189-9979. The author would like to thank his colleagues Dr. Paul Reynolds and Dr Donald Nyawako from the University of Sheffield, and Mr Carlos Casado and Mr Jesús de Sebastián from CARTIF Centro Tecnológico for their collaboration in works presented in this chapter.
Titanium dioxide (TiO2) is a multifunctional, semiconductor and polymorphic material, which is commercialized in rutile or anatase phases, both in tetragonal crystal structures. TiO2 is used in industry since 1918 as pigment in paints, paper, plastic, drugs, cosmetics, etc. In the last years, with the beginning of nanotechnology, powder and films of titanium dioxide have been widely studied due to its new properties obtained by decreasing the particles size. The wide range of application is due to its electronic and structural properties, such as high transmittance in the visible, high refractive index (n = 2.6), high photocatalytic activity, and chemical stability. These properties make TiO2 an excellent material for use in photocatalysis, antimicrobial surfaces, self-cleaning and hydrophobic surfaces, photovoltaic cells, gas sensor, photochromic devices, etc. .\n
Titanium is the second transition metal on the periodic table and has Ar-3d24s2 distribution. It was discovered in 1791 by the mineralogist William Gregor, in the region of Cornwall, United Kingdom, in the mineral ilmenite (FeTiO3). In 1795, it was isolated by the German chemist Heinrich Klaproth in the form of TiO2 rutile phase. Titanium dioxide can be found in three different crystalline phases: anatase, brookite, and rutile. By thermal treatment, it is possible to convert the anatase and brookite phases in rutile, which is thermodynamically stable at high temperatures. The anatase phase is more reactive, mainly in nanometric dimension, and is frequently used in photocatalytic applications.\n
As semiconductor, TiO2 can be studied in terms of the energy band theory, whose bandgap energy (3.2–3.6 eV) can be supplied by photons with energy in the near ultraviolet range and whose separation between valence and conduction bands is intrinsically linked with its optical and electronic properties. These bandgap values depend on the particle size, phase, and used dopant, making possible the modulation of these values. In the case of thin films, which traditionally are formed by TiO2 nanoparticles, the thickness also contributes to the modulation of the bandgap values. Several studies are made aiming the best quality of the films and the decrease in the bandgap energy by introduction of dopants in the TiO2 structures to improve the photocatalytic propriety in the visible region of the light [1, 2].\n
The introduction of dopants in the TiO2 thin film structure such as SiO2, Ag, and Nb, among others, changes its properties expanding the range of possible applications. The methods of preparation also influence significantly its morphology, structure, and texture, modifying its properties. Several methods can be used to obtain thin films such as chemical vapor deposition, sputtering, spray pyrolysis, and sol-gel process. The sol-gel process  allows the preparation of thin films with high purity, thermal and mechanical resistance, chemical durability and the control of morphology, composition, thickness, and porosity. Thin film depositions using the sol-gel process can be realized by dip-coating, spin-coating, or spray-coating techniques. These techniques are economically feasible and can be applied to substrates with large surfaces and different forms.\n
The sol-gel process  that leads to the formation of TiO2 films is based on mechanisms of hydrolysis and polycondensation of titanium alkoxides mixed with alcohol and catalytic agents. There are various kinds of Ti alkoxides such as titanium isopropoxide (Ti(OiPr)4) and titanium ethoxide (Ti4(OEt)16), among others, that need to be used preferentially with their correspondent alcohol. The precursor solution, also called sol, is a colloidal suspension of Ti surrounded by ligands, with physical-chemical properties adequate to the formation of a film. After a deposition, which can be by dip-coating, spin-coating, and spray-coating processes, the film is formed by a wet gel that became a dry gel after drying process. The hydrolysis of the alkoxide group to form Ti─OH occurs due to nucleophilic substitution of O─R groups (alkyl group) by hydroxyl groups (─OH) and the condensation of the group Ti─OH, to produce Ti─O─Ti and by-products (H2O and ROH), leading to formation of the gel, according to the equation below:\n
This mechanism is relatively complex because the reactions occur simultaneously during the process of deposition. In this proposed mechanism, the alkoxide precursor passes by the sequences, oligomer, polymer, and colloid, and it finishes as an amorphous porous solid structure. Thermal treatments are used for the preparation of nanocrystalline thin films. With the use of doping salts in the precursor solutions, the mechanism becomes more complex due to the introduction of other metals in the gel network.\n
The dip-coating technique  consists into dip a substrate in the sol and removes it at constant speed (Figure 1), resulting in an M─O─M oxide network that forms a wet gel film. The network structure, the morphology, and the thickness of the film depend on the contributions of the reactions of hydrolysis and condensation that must occur in approximately the same velocity of substrate withdrawal. Otherwise, the solution may run down the substrate. These properties may be controlled varying the experimental conditions: type of organic binder, the molecular structure of the precursor, water/alkoxide ratio, type of catalyst and solvent, withdrawal speed, and solution viscosity. After the deposition, the gel film is formed by a solid structure impregnated with the solvent, and a drying process can be used to convert the wet gel in a dry porous film. Denser film can be tailored by different temperatures of thermal treatment, leading to films with different specific surface areas and porosities.\n\n
The advantage of the dip-coating process is the ease of deposition in substrates of any size and shape, facilitating the industrial process.\n
TiO2 thin films were prepared by sol-gel process [2, 5] using titanium isopropoxide (Aldrich, 98%) as the precursor of titania mixed with isopropyl alcohol and hydrochloric acid in stoichiometric amounts. The precursor solution was kept under agitation at room temperature for 1 h and rested until the viscosity reaches the best value condition, between 2 and 5 cP. The films were prepared using solutions with 2 < pH < 4 and atmosphere relative humidity <40%, since they are opaque and not adherent for other pH and relative humidity values. The films were deposited onto clean substrates (borosilicate glass, steel, silicon, and magnets) at room conditions (25°C, relative air humidity lower than 30%), using a dip-coating equipment with withdrawal speed between 0.2 and 1.5 mm/s. The substrates were washed with standard cleaning method before dipping. After each dip-coating process, the wet films were dried in air for 30 min and thermally treated at temperatures between 100 and 500°C for a range of time (between 10 and 60 min) to convert them into porous or densified oxide films. Depending on the thermal treatment temperature, the films can be amorphous or nanocrystalline. Some samples were submitted at UV-C light (lamp Girardi RSE20B, 254 nm—15 W) to crystallize without increasing the temperature. Crystalline structures were investigated by an X-ray diffraction (incidence angle of 5°) using a diffractometer Rigaku (Geigerflex model 3034). The samples were analyzed by atomic force microscopy (AFM) in an Asylum Research, model MFP-3D-SA, to observe the topography and possible coating defects, such as cracks and peeling. Morphological characterization was evaluated by transmission electron microscopy (FEI TECNAI G2 20 at acceleration tension of 200 kV). Electron diffraction was also used to determine the structure of the crystalline phases. The films were pulled from glass substrates and mounted onto 200 mesh copper grids coated with holey carbon films for examination. The morphology and composition were evaluated by a scanning electron microscope (SEM) FEI Quanta 200 FEG with an energy-dispersive spectrometer (EDS). The transparency and thickness of the films deposited on glasses were verified by the optical transmission spectra measured with an ultraviolet and visible spectrometer (U3010, Hitachi).\n
The TiO2 films obtained by sol-gel process using the dip-coating technique are transparent, homogeneous, adherent, durable, and free of micro-cracks. Figure 2a shows thin films removed from a glass substrate. The thickness of the films deposited in glass and dried in air can range from 40 to 800 nm for each coating, depending on the withdrawal speed and viscosity. After heating, the film thickness decreases due to the densification process, reaching values between 20 and 300 nm each coating. When the number of coating increased, the thickness can reach 800 nm after calcination without cracks.\n\n
After drying, the films are porous when treated at low temperatures, and the density increases as a function of heating temperature and time. The porosity of the films leads to a variation in the refraction index that can change from 1.9 to 2.3 (λ = 550 nm) for porosities between 20 and 5%, respectively. Figure 2b shows an example of the variation of thickness and refractive index in the function of thermal treatment temperature of TiO2 film. When the TiO2 films are deposited in substrates that cannot be thermally treated, such as polymers and cotton, the densification and crystallization can be made by UV light treatment. Figure 3 shows images of TiO2 films heated at 100 and 400°C for 10 min.\n\n
The film formed after drying at room temperature is amorphous and contains organic contaminants in the network. With increasing in temperature of thermal treatment, the film structure changes to anatase phase around ~300°C and to rutile phase above ~600°C.\n
According to the literature, the values of the phase transition of TiO2 can change in some degrees also depending on the type and time of drying, used dopant, and particle size, among others factors. Figure 4 shows typical diffractograms of TiO2 films deposited in glass substrate in two temperatures, generating an amorphous material at 100°C and a nanocrystalline material at 400°C. Figure 5 shows SEM and TEM images of the film and the respective electron diffraction that confirm its anatase phase.\n\n\n
TiO2 thin films are used in the confection of optical devices (linear and nonlinear) due to the transparency throughout the visible spectrum, high linear and nonlinear refractive index that change in function of the wavelength, and dielectric properties. Their nonlinearity can make possible operations such as logic, all-optical switching, and wavelength conversion. Their high linear index of refraction can improve optical confinement as waveguide. The optical and electric properties of the thin films made by sol-gel process can be modulated according to the desired application. Figure 6 shows transmittance curves of TiO2 thin films deposited on glass substrates as a function of the number of layers. Each layer measures approximately 60 nm.\n\n
By these spectra it is possible to calculate the bandgap of the films using, for example, the Tauc method. The value measured in this case was 3.4 eV, meaning that the photocatalytic activity occurs at a wavelength in the UV region. Several studies are made aiming to reduce the bandgap of the TiO2 anatase phase to the visible region to make it a competitive energy source with application in photocatalysis, solar cells, and artificial photosynthesis.\n
TiO2 films are also used in the preparation of hydrophobic and self-cleaning surfaces in several substrates. Figure 7 shows water drops over the film surface and over the glass substrate surface. The contact angle can be change varying the film porosity and the number of layers, for example.\n\n
The TiO2 self-cleaning surfaces have the ability to remove greasy dirt and bacteria from their surfaces due to their photocatalytic property, which promotes the breakdown of fat molecules or destroys the membranes of bacteria. The self-cleaning property is frequently connected to hydrophobic surfaces, because the dusts can be removed by the rolling of the water droplets in the surface.\n
When Si alkoxide is mixed with Ti alkoxide to the preparation of precursors of TiO2/SiO2 thin films for utilization of the sol-gel process, the nanocomposites produced can combine or enhance the properties of the well-known pure oxides: TiO2 and SiO2 . These nanomaterials can offer enhanced photocatalytic activities, persistent superhydrophilicity, modulated refractive index, enhanced resistance to corrosion, and superior mechanical properties such as larger mechanical resistance and hardness. The deposition of TiO2/SiO2 thin films in different substrates such as glasses, metals, ceramics, and polymers enables the application of these films in many purposes such as self-cleaning surfaces, antireflection surfaces, anticorrosion protection, wear resistance protection, fungicide and bactericide surfaces, water and air treatment devices, planar waveguides, nonlinear optical devices, etc. The most important fact is that two or more of these applications can be combined in TiO2/SiO2 multifunctional surfaces [7, 8].\n
In this work, the preparation of TiO2/SiO2 nanocomposite thin films was made using titanium isopropoxide (Aldrich, purity >98%), isopropyl alcohol and hydrochloric acid, to prepare the TiO2 precursor solution and tetraethyl orthosilicate (Aldrich, purity >98%), isopropyl alcohol, hydrochloric acid, and distilled water to prepare the SiO2 precursor solution. The pH of both solutions was maintained in 3. SiO2 precursor solution was refluxed for 24 h at 60°C. Both the prepared solutions were aged for 24 h before the mixture. Then, TiO2/SiO2 precursor solutions with different xTiO2/(100-x)SiO2 molar ratios (x = 0, 20, 40, 60, 80, and 100%) were prepared and stirred for 1 h. The final viscosity of the solutions was maintained in approximately 2.2 cP. The films were deposited on properly clean glass substrates with a constant withdraw speed of 1.0 mm/s at 25°C and relative air humidity about 30%. The drying process occurred at 80°C in air for 10 min. This stage (deposition and drying) was repeated five times for thickness control. Finally, the samples were thermally treated at 500°C for 1 h.\n
The TiO2 thin films were formed by anatase phase, and the SiO2 thin films were amorphous according to XRD patterns and Raman spectroscopy results. The TiO2/SiO2 thin films are formed by the anatase phase dispersed in a vitreous matrix. The anatase phase is fundamental for the desired applications due to their optical and photocatalytic property. The microstructure, morphology, and texture of the xTiO2/(100-x)SiO2 thin films change substantially due to the mixture of the titanium and silicon oxide, as seen in AFM images of Figure 8.\n\n
With the addition of SiO2, the titania nanoparticles remain dispersed in the vitreous matrix, and because of that, TiO2 and SiO2 pure films have higher root-mean-square (RMS) roughness (2.2 and 6.0 nm, respectively) than TiO2/SiO2 films (between 0.2 and 1.2 nm). The surface smoothing, after the mixture of TiO2 and SiO2, resulted in an enhanced hardness that changes to 4.5 GPa for both pure films and to approximately 7.4 GPa for all nanocomposite thin films. These properties are essential for outdoor applications, special windows, glasses of cars, and other vehicles, among others, since the film surfaces can be subjected to intense mechanical wear of air particles. Moreover, TiO2/SiO2 nanocomposite thin films present a persistent superhydrophilicity, which is required for application on self-cleaning surfaces and water/air treatment, promoting a better washing of the contaminants in the surface, which can be obtained with the rain precipitation. These nanocomposites increase the adsorption of pollutants by the surface.\n
The optical properties of the xTiO2/(100-x)SiO2 films are modulated by Ti/Si rate variation, as seen in Figure 9.\n\n
The possibility to modulate the transmittance and refractive index (n) of the xTiO2/(100-x)SiO2 thin films is essential in applications as antireflection surfaces, filters, and planar waveguides, since this wide variation of n (from 1.45 to 2.18 in visible light) permits the construction of different structural models of devices. The variation in the refraction index in function of incident light wavelength of 2.0–2.8 (Figure 9b) is also very important to the construction of nonlinear optic devices .\n
TiO2 exhibits a high energy bandgap (3.2–3.8 eV) which corresponds to UV irradiation with a wavelength smaller than 388 nm. To overcome this limitation, several studies have been performed showing the modification of TiO2 with metal and nonmetal species aiming to extend the light absorption to the visible range and simultaneously increasing the recombination time of the electron-hole pairs formed. In particular, nanocomposite thin films of silver and titania have been of considerable interest since silver nanoparticles can act as electron traps, contributing to electron-hole separation and creating a local electric field capable of facilitating the electron excitation and consequently their photocatalytic properties. The improvement in the photocatalytic properties leads to surfaces with better bactericide, hydrophobicity, and self-cleaning characteristics .\n
Ag/TiO2 coatings were prepared from alcoholic solution containing titanium isopropoxide and silver nitrate dissolved in a mixture of isopropyl alcohol in several atomic ratios. Acid conditions (pH = 4) were reached after acetic acid addition. This precursor solution was stirred at room temperature during 1 h and submitted to UV-C irradiation (254 nm) treatment in air for 100 min. This procedure has been used to produce metallic Ag from Ag+ ions. The films were deposited onto clean substrates as borosilicate, silicon, 316 L stainless steel, and magnets (NdFeB) with withdrawal speed of 8 mm s−1. After deposition, the coatings with one to five layers were dried in air for 20 min and were thermally treated for 1 h between 100 and 400°C [5, 11].\n
Figure 10 shows the characteristic diffractogram of Ag/TiO2 thin films with five layers deposited on glass and heated at 400°C.\n\n
According to XRD patterns, the coatings heated at 400°C show indexed peak characteristic of crystalline metallic Ag and anatase phase (PDF #1-562). The diffractogram of the film heated at 100°C was characteristic of a noncrystalline material, as expected. The substrates of 316 L stainless steel and magnets showed similar XRD patterns. SEM images of Ag/TiO2 heated at 400°C deposited on different substrates are shown in Figure 11.\n\n
The structure of the used substrates has induced the formation of nano- and microstructures of metallic silver with different sizes and morphologies supported on the TiO2 thin film surfaces. This formation occurs due to thermal treatment that induces the diffusion of the metal nanoparticles to the film surface. In the borosilicate substrate (Figure 11a), the formation of spherical Ag nanoparticles with a bimodal particle size distribution is observed. When substrates of 316 L stainless steel and magnets (NdFeB) were used, Ag dendrite micro- and nanostructures were formed (Figure 11b and c). A trimodal size distribution is observed for the particles present on the surface of the Ag/TiO2 film deposited on silicon (Figure 11d). Particularly in this film, the Ag particles show dimensions of 5–150 nm.\n
Energy-dispersive spectra (EDS) shown in Figure 12 has confirmed the elemental composition of the Ag/TiO2 films treated at 400°C deposited on 316 L stainless steel. In this film’s circular, micrometric and submicrometric structures also are observed besides the dendrites mentioned above. Brightness regions on the micrograph are constituted only by Ag, while the other regions are formed by TiO2 matrix in the anatase phase, according to the XRD results. The analyses for the other substrates were similar.\n\n
Figure 13 shows AFM images of Ag/TiO2 thin films with one layer deposited on 316 L stainless steel substrate. The surface roughness of the 316 L stainless steel, whose texture is shown in Figure 13a and b, is ~40 nm, a much higher value compared to the roughness value of the borosilicate substrate, which is about 0.20 nm. It is observed that the Ag/TiO2 films deposited on the steel substrates reduce their roughness as a function of the number of layers deposited. With four layers, the roughness value decreases to 7 nm. In addition, the Ag/TiO2 films are formed by silver nanoparticles dispersed on the surface of the TiO2 matrix with sizes between 20 and 50 nm.\n\n
The introduction of silver in the TiO2 structure changes their optic properties as can be seen in Figure 14a, represented by the variation of transmittance in the function of wavelength. The bandgap decreases, depending on the amount of silver in the crystalline structure (Tauc method), until values of 1.75 eV depend on the concentration of silver, according to the literature .\n\n
Figure 14b shows the absorption spectra of pure and doped TiO2, emphasizing the photonic property of the Ag/TiO2 thin films, with absorption peaks between 490 and 520 nm that changed with the variation of the molar ratio (Ag:Ti). These photonic surfaces provide new possibilities to increase the efficiency of solar energy conversion by confinement of the light, improve bandgap effects, and enhance optical transmission as well as nonlinear optical switching in surface polaritonic structures.\n
Other utilizations of Ag/TiO2 thin films are in hydrophilic/hydrophobic surfaces and in bactericide and fungicide devices , since the silver increases the TiO2 efficiency.\n
Traditionally, the niobium is used mainly in the confection of metallic alloys for several industrial applications . However, the use of niobium to produce ceramic materials is increasing in the last few years with several applications into catalysis, supercapacitor, and battery components, among others. The incorporation of the niobium in other material structures, causing substitutional defects, has been studied to improve several material properties, such as TiO2. Examples of applications of Nb-doped TiO2 are its use as photocatalyst, dye-sensitized solar cells, gas sensors, magnetic properties, and transparent conductive oxide (TCO) for several electronic devices.\n
Several methods are being used to synthesize and deposit Nb-doped TiO2 thin films in different types of substrates. However, the most used deposition methods are chemical vapor deposition (CVD), sputtering, and sol-gel process. In the sol-gel synthesis of Nb-doped TiO2, the use of mainly two niobium precursors, niobium ethoxide [Nb(OCH2CH3)5], and niobium pentachloride (NbCl5) that are very expensive is reported in the literature . In this work, Nb/TiO2 coatings were prepared from alcoholic solution containing titanium isopropoxide and ammonium-(bisaquo oxobisoxalato) niobate-trihydrate (produced by CBMM, Brazil) dissolved in a mixture of isopropyl alcohol. Acid conditions (pH = 4) were reached after acetic acid addition. The precursor solution was stirred at room temperature during 1 hour and deposited by dip-coating process in clean glass substrates with withdrawal speed between 0.8 and 3.7 mm s−1. After deposition, the coatings with one to five layers were dried in air for 20 min and were thermally treated for 1 h between 100 and 500°C.\n
The Nb-TiO2 thin films obtained are transparent, adherent, free of micro-cracks, and with visual appearance more homogeneous than the other deposited thin films. The niobium increases the mechanical resistance of the surface.\n
A theoretical study using density functional theory (DFT) showed that the insertion of niobium in the titanium dioxide matrix, causing the substitution of Ti4+ cations for Nb5+ cations, changes its lattice parameters, cell volume, and bandgap . Therefore, the structures of the materials calcined at 500°C were found to be crystalline in the anatase phase (PDF #1-562). The thin films doped with 0.5, 1, and 3% molar ratio Nb:Ti showed a displacement of the 101 and 200 peaks to lower angles, evidencing the substitution of the niobium inside the crystal structure, as shown in Figure 15.\n\n
The increase of niobium content in the thin film promoted a considerable variation in the lattice parameters, whose d101 changed to 3.49 for pure TiO2 and to 3.55 for 3% Nb/TiO2. The crystallite size decreased from 11 to 7 nm, which agreed with the DFT results previously reported.\n
AFM 3D micrographs (Figure 16a and b) show that the TiO2 has larger particle size and RMS roughness of 2.2 ± 0.1 nm, while the 2% Nb/TiO2 film presents a RMS roughness of 0.6 ± 0.2 nm and smaller nanoparticles. All Nb/TiO2 thin films presented different profiles than TiO2 thin films, with smaller nanoparticles and RMS roughness and, therefore, more homogeneity, adherence, and visual quality.\n\n
UV-Vis spectra seen in Figure 17 show that also it is possible to modulate the transmittance of the thin films as a function of the wavelength to obtain optical filters. All studied films showed similar bandgap values obtained by the Tauc method, between 3.6 and 3.4 eV. The insertion of niobium on the TiO2 structure led to a denser film with higher refractive index and high mechanical resistance.\n\n
The sol-gel deposition parameters such as the density of the precursor solution, concentration of oxides, viscosity, withdrawal velocity, number of dips, and drying temperature influence the characteristics of the films such as thickness, porosity, refractive index, particle size, particle shape, and oxidation degree. Someway, all dopants used improved the quality and the range of application of the TiO2 films. The addition of SiO2 in the TiO2 films changes their mechanical, optical, and surface properties. The addition of Ag increases its photocatalytic activity, improving fungicide and bactericide properties of the films. The hydrophobicity/hydrophilicity change capacity was improved too. The doping with Nb improves the mechanical resistance of the films. All these properties can be applied in the confection of best photocatalytic surfaces to be used in the production of solar energy, self-cleaning surface, and optical and nonlinear optical devices.\n
The authors would like to thank FAPEMIG, CNPq, and CAPES for their financial support and UFMG’s Microscopy Center for the images.\n