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

Abstract

Using a C 1 QUAD-8 shear-flexible plate element, based on a new kind of kinematics which allows one to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers in the laminates, the non-linear instability behaviour of plates subjected to periodic in-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 geometrically non-linear parametric instability characteristics of isotropic and composite plates through a finite element formulation with dynamic response analysis. The non-linear governing equations obtained here are solved using the Newmark integration scheme coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the phenomenon, which are known from experiments, i.e. existence of beats, their dependency on the forcing frequency, the influence of initial conditions and load amplitudes, and the typical character of vibrations in the different regions.