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.