Vibration analysis of fluid-filled functionally graded material (FGM) cylindrical shells (CSs) is investigated with ring supports. The shell problem is formulated by deriving strain and kinetic energies of a vibrating cylindrical shell (CS). The method of variations of Hamiltonian principle is utilized to change the shell integral problem into the differential equation (DE) expression. Three differential equations (DE) in three unknown for displacement functions form a system of partial differential equations (PDEs). The shells are restricted along the thickness direction by ring supports. The polynomial functions describe the influence of the ring supports and have the degree equal to the number of ring supports. Fluid loaded terms (FLT) are affixed with the shell motion equations. The acoustic wave equation states the fluid pressure designated by the Bessel functions of first kind. Axial modal deformation functions are specified by characteristic beam functions which meet end conditions imposed on two ends of the shell. The Galerkin method is employed to get the shell frequency equation. Natural frequency of FGM cylindrical shell is investigated by placing the ring support at different position with fluid for a number of physical parameters. For validity and accuracy, results are obtained and compared with the data in open literature. A good agreement is achieved between two sets of numerical results.
Part of the book: Computational Fluid Dynamics
This chapter is concerned with the vibration analysis of single-walled carbon nanotubes (SWCNTs). This analysis is based on the Donnell thin shell theory. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. Vibration frequency spectra are gained and evaluated for physical parameter like length-to-diameter ratios. The dimensionless frequency is also investigated in armchair and zigzag SWCNTs with in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs. These frequencies of the SWCNTs are computed with the aid of the computer software MATLAB. These results are compared with those obtained using molecular dynamics (MD) simulation and the results are somewhat in agreement.
Part of the book: Novel Nanomaterials
In this chapter, vibrations of isotropic rectangular plates have been analyzed by applying the wave propagation approach. The plate problem has been expressed in integral form by considering the strain and kinetic energies. The Hamilton’s principle has been applied to transform the integral form into the partial differential equation of second order. The classical method namely product method has been used to separate independent variables. The partial differential equation has converted into the ordinary differential equations. The axial wave numbers are associated with particular boundary conditions. This is an approximate technique, which is based on eigenvalues of characteristic beam functions. The natural frequencies of plates are investigated versus modal numbers by varying the length and width of the plates with simply supported-simply supported (SS-SS), clamped-clamped (CC-CC), and simply supported-clamped (SS-CC) boundary conditions. The frequencies of the plates increase by increasing the modal number, and CC-CC frequencies are greater than the frequencies of other boundary conditions. Computational computer software MATLAB is engaged to characterize the frequencies. The results are compared with the earlier simulation work in order to test the accuracy and efficiency of the present method.
Part of the book: Advanced Engineering Testing