Post-Buckled Vibration Characteristic of Composite Cylindrical Shell Panels Under Parabolic In-Plane Edge Compression

Abstract

In this paper, post-buckled vibration of cross-ply thick laminated cylindrical shell panels subjected to nonuniform (parabolic) uniaxial and biaxial compression is studied. The mathematical model is based on a higher order shallow shell theory incorporating von Kármán-type geometric nonlinearities and initial geometric imperfections. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the plate in the pre-buckling range as the applied in-plane edge load is nonuniform. By using the above stress distributions, the governing shell panel post-buckling equations are derived through Hamiltonian principle. The governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations for post-buckling analysis and nonlinear ordinary differential equations in the case of free vibration analysis using Galerkin's method. The equilibrium paths through limit points are traced using Newton–Raphson method in conjunction with Riks approach. The free vibration frequency of pre-bucked and post-buckled cylindrical panels loaded with uniaxial or biaxial nonuniform in-plane edge load are studied. Free vibration frequency for symmetric (0/90/0) cross-ply laminated cylindrical shell panels under uniaxial and biaxial parabolic in-plane load with initial imperfections are presented for different post-buckled deflections. Limit loads and snap-through behavior of shell panels and corresponding free vibration results are co-related for better understanding of the problem.