THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE
复合材料层合板1:1参数共振的分岔研究

A simply supported rectangular symmetric cross-ply laminated composite plate with parametric excitation is considered. The governing equations of motion for the laminated composite plate are derived by means of von Karman equation. The material nonlinearity, geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin's approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to first-order averaged equations. The averaged equations are numerically solved to obtain the bifurcation responses find to analyze the stability for the laminated composite plate. Under certain conditions the laminated composite plate may occur two non-steady-state bifurcation solutions and jumping phenomena. The bifurcation and chaotic motion of the rectangular symmetric cross-ply laminated composite plate is simulated numerically. The effect of the Galerkin's truncation to nonlinear dynamic analysis is presented. The way of the system going into chaos is also investigated and explained.