带初始几何缺陷FGM固支圆柱壳的非线性动力学分析

NONLINEAR DYNAMICS ANALYSIS ON FGM CLAMPED-CLAMPED CIRCULAR CYLINDRICAL SHELLS WITH INITIAL GEOMETRICAL IMPERFECTION

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.

Nonlinear dynamics analysis on clamped-clamped FGM circular cylindrical shell containing initial geometrical imperfections with different volume fraction under different temperatures is conducted in this paper. The effective properties of FGM circular cylindrical shell are supposed to be gradiently distribu- ted in thickness direction. Based on the classical shear deformation theory and von-Karman type nonlinear strain-displacement relationship,combined with Hamilton＇s principle,the nonlinear partial differential gov- erning equations of motion for the clamped-clamped FGM circular cylindrical shell are obtained. Consider- ing the symmetric mode of clamped-clamped circular cylindrical shell,the Galerkin＇s method is utilized to discretize the governing partial equations,and then the differential form of nonlinear dynamics equation is derived. The Runge-Kutta method is applied for numerical simulation,and the maximum lyapunov index is plotted. The influences of the plane loads ,imperfection volume fraction and temperature on the nonlinear dynamics are studied in details, respectively.