Effect of boundary constraint on the frequency response of moderately thick doubly curved cross-ply panels using mixed fourier solution functions

A hitherto unavailable analytical solution to the boundary value problem of free vibration response of shear-flexible cross-ply laminated doubly curved panels is presented. The laminated shell theory formulation is based on the first-order shear deformation theory (FSDT) including rotatory and surface-parallel inertias. The governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns - three displacements, and two rotations. The assumed solution functions for the eigen/boundary-value problem are selected in terms of mixed-type double Fourier series. Extensive numerical results that are presented in this study include (1) convergence characteristics of computed natural frequencies, and (2) effects of length-to-thickness ratio, radius-to-length ratio, lamination sequence, boundary constraint and shell geometry on the normalized natural frequencies of interest. Also numerically investigated is the highly complex interaction among bending-stretching type coupling effect, membrane action due to shell curvature, surface-parallel end constraints (or lack thereof), and the effects of transverse shear deformation, rotatory inertias and surface-parallel inertias.