复合材料层合板1:1参数共振的分岔研究

针对复合材料对称铺设各向异性矩形层合板的物理模型,在同时考虑了材料、阻尼和几何等非线性因素后,建立了二自由度非线性参数振动系统动力学控制方程,并应用多尺度法求得基本参数共振下的近似解析解,利用数值模拟分析了系统的分岔和混沌运动.指出了伽辽金截断对系统动力学分析的影响,以及系统进入混沌的途径.

THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE

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.