Non-linear forced vibrations of antisymmetric rectangular cross-ply plates

Abstract

A method of direct numerical integration of the frequency/time period expression is proposed to study the non-linear forced/free vibration behaviour of rectangular, antisymmetric cross-ply plates. The presence of bending-extension coupling in such plates results in a cubic non-linear term in addition to a fourth power term in the energy balance equation. The existence of this term does not allow two real and opposite roots at a maximum amplitude position unlike in isotropic, orthotropic, symmetric cross-ply, square antisymmetric cross-ply and symmetric and antisymmetric angle-ply plates, but such an energy balance equation definitely has two real roots, which are unequal in magnitude and different in sign. The extensively used perturbation method fails to predict the response of such plates, depending on the severity of the bending-extension coupling. The proposed direct integration method, even with single-term approximations for in-plane and transverse displacements, yields consistently accurate results. Response curves for several configurations of antisymmetric, simply supported rectangular cross-ply plates are presented.