Nonlinear oscillations and chaotic dynamics of an antisymmetric cross-ply laminated composite rectangular thin plate under parametric excitation

Abstract

In this paper, nonlinear oscillations and chaotic dynamics of a simply supported antisymmetric cross-ply laminated composite rectangular thin plate under parametric excitation is investigated for the first time. The governing equations of motion for the antisymmetric cross-ply laminated composite plate are derived by using von Karman-type plate equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. A two dof parametrically excited nonlinear system including the quadratic and cubic nonlinear terms is obtained by using the Galerkin method. Based on the Fourier expansion and the temporal rescaling, an asymptotic perturbation method is utilized to obtain four-dimensional nonlinear averaged equations on the amplitude and the phase of nonlinear oscillations of the antisymmetric cross-ply laminated composite plate. Based on the averaged equations, the steady-state nonlinear responses and their stabilities are determined by using numerical approach. The relations between the steady-state nonlinear responses and the amplitude and frequency of parametric excitation are obtained. Under the certain conditions, the antisymmetric cross-ply laminated composite plate may have two steady-state nonzero solutions in which the jumping phenomenon occurs. Numerical simulation is used to discover the periodic and chaotic motions in the antisymmetric cross-ply laminated composite rectangular thin plate. It is observed from the numerical results that the multipulse orbits exist in the antisymmetric cross-ply laminated composite rectangular thin plate.