Free Vibration Response of Cylindrical Panels With Higher Order Shear Deformation Theory

Presented here is an analytical solution to the free vibration problem of an isotropic cylindrical panel with SS2-type simply supported boundary conditions based on Reddy's third order shear deformation shell theory. Using the principle of virtual work, the Reddy's shell theory generates five highly coupled partial differential equations in terms of three unknown displacements and two unknown rotations. The partial differential equations in conjunction with the prescribed boundary conditions are solved using displacement functions expressed in terms of double Fourier series expansion. Cylindrical panels with various aspect and thickness ratios are considered in the study of convergence behavior and parametric variation of the eigenvalues. The eigenvalues and mode shapes obtained in this study are compared with those obtained from the finite element software package ANSYS. The hitherto unavailable analytical solutions can be used as benchmarks for checking the accuracy of various approximate methods such as the Rayleigh–Ritz, finite element and finite difference methods.