Analysis of Nonlinear Dynamics and Bifurcations for a Rectangular Symmetric Cross-Ply Laminated Composite Plate with a Parametric Excitation

Abstract

Using the analytical and numerical approaches, the nonlinear dynamic behaviors in the vicinity of a compound critical point are studied for a rectangular symmetric cross-ply laminated composite plate with a parametric excitation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion in this model. Normal form theory, bifurcation and stability theory are used to find closed form solutions for equilibria and periodic motions. Stability conditions of these solutions are obtained explicitly and critical boundaries along which incipient and secondary leading to 2-D tori are also derived. Finally, numerical results are presented to confirm these analytical predictions.