Nonlinear Oscillations of an Antisymmetric Cross-Ply Laminated Composite Thin Rectangular Plate Under Parametric Excitation

In this paper, nonlinear dynamics of a simply supported antisymmetric cross-ply laminated composite thin rectangular plate under parametric excitation is investigated. 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-degree-of-freedom 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 obtained four-dimensional nonlinear averaged equations on the amplitude and the phase of nonlinear oscillations of the antisymmetric cross-ply laminated composite plate for the first time. 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.