中文摘要：

根据复合材料特性、梁的几何非线性和哈密尔顿原理,建立了复合材料薄壁梁的模型及非线性平衡方程.基于悬臂梁的边界条件,对非线性自治系统进行有限差分离散处理,得到了系统的质量和刚度矩阵.运用MATLAB振动工具箱进行模态分析,求得CUS和CAS架构下薄壁箱梁的前三阶固有频率与铺层角的变化关系,并对两种架构下的结果进行对比分析.在有限差分离散的基础上建立非线性薄壁梁的状态空间,运用时间离散和MATLAB振动工具箱对非线性自治系统进行仿真,求得CUS架构下不同铺层角度时的时间位移曲线和非线性振动幅度与铺层角之间的变化关系.

英文摘要：

According to the characteristics of composite material,geometric nonlinearity of beams and Hamilton principle,the model of composite thin-walled beams and the nonlinear equilibrium equations were established.Based on the boundary conditions of cantilever beams,the mass and stiffness matrices of the nonlinear autonomous system can be obtained using a finite difference method.The relationships between the first three order natural frequencies and ply angles can be gotten by the MATLAB vibration toolbox,and the two results under CUS and CAS configurations were analyzed.The state space equations were simulated by time？discretion and the MATLAB vibration toolbox.The time-displacement curves of the composite beam tips and the amplitude curves of the nonlinear vibration during changing ply angles were drawn under CUS configuration.