Nonlinear static and dynamic damped response of isotropic, elastic circular plates

Abstract

Nonlinear static and dynamic response analysis of clamped-in and simply supported boundary conditions, and immovably constrained and stress-free edge conditions for circular plates of isotropic elastic material with damping, subjected to step pressure pulse excitation are presented. The Von Karman relations are used which are reduced to coupled nonlinear partial differential equations and solved by a one-term solution, applying the Ritz-Galerkin technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation technique. Plots of static deflection to thickness ratio versus non-dimensional load for different boundary and edge conditions, and the effect of damping on the nonlinear dynamic response for different values of non-dimensional damping factor are presented.