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论文主要研究了带初始几何缺陷的功能梯度固支圆柱壳在不同体积分数和温度下的非线性动力学行为.假定该功能梯度圆柱壳材料的组分是沿厚度的方向呈梯度变化的.运用经典板壳理论、von-Karman几何非线性应变位移关系以及Hamilton原理,推导出两端固支FGM圆柱壳的偏微分非线性运动控制方程.论文考虑了圆柱壳的对称模态,利用Galerkin法对上述非线性动力学方程进行截断,得到常微分形式的非线性动力学方程.主要运用Runge-Kutta法进行数值仿真,并且画出了其最大lyapunov指数图,主要研究了面内载荷对振动响应的影响,并分别对比了不同体积分数和温度对系统非线性动力学的影响.
In the paper, the nonlinear dynamic behavior of a functionally graded cylindrical cage with initial geometric defects at different volume fraction and temperature is studied, and the composition of the functionally graded cylindrical shell material is assumed to be gradient along the thickness direction. Classical shell theory, von-Karman geometric nonlinear strain displacement relationship and Hamilton principle, the partial differential nonlinear motion equations of cylindrical shell with both ends fixed and fixed are deduced.The symmetry modal of cylindrical shell is considered and the Galerkin method The above nonlinear dynamics equations are truncated to obtain the nonlinear dynamics equations in the form of ordinary differentials.The Runge-Kutta method is used to conduct the numerical simulation and the maximum Lyapunov exponent is plotted. The effects of the in-plane loads on the vibration response The effects of different volume fraction and temperature on the nonlinear dynamics of the system were compared.