Non-linear dynamic stability characteristics of elastic plates subjected to periodic in-plane load

Using a C-1 QUAD-8 shear-flexible plate element, based on a new kind of kin ematics which allows one to exactly ensure the continuity conditions for di splacements and stresses at the interfaces between the layers in the lamina tes, the non-linear instability behaviour of plates subjected to periodic i n-plane load has been studied. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. Primarily, an attempt is made here to understand the geome trically non-linear parametric instability characteristics of isotropic and composite plates through a finite element formulation with dynamic respons e analysis. The non-linear governing equations obtained here are solved usi ng the Newmark integration scheme coupled with a modified Newton-Raphson it eration procedure. The analysis brings out various characteristic features of the phenomenon, which are known from experiments, i.e. existence of beat s, their dependency on the forcing frequency, the influence of initial cond itions and load amplitudes, and the typical character of vibrations in the different regions. (C) 1999 Elsevier Science Ltd. All rights reserved.