旋转薄壁圆柱壳非线性波动振动分析

Forced nonlinear wave vibration of clamped-free rotating thin cylindrical shell

基于Donnell’s简化壳理论,考虑阻尼和几何非线性,建立旋转薄壁圆柱壳在法向激振力作用下的波动振动方程,并利用Galerkin方法将波动振动方程转换到模态坐标上,其中考虑到一端自由一端固支的边界条件,节径数和轴向半波数分别取为6和1,得到2个相互耦合的非线性微分方程,用数值方法研究了各模态变量的时间响应和非线性幅频特性,并讨论了振动响应的稳定性和激振力对系统非线性的影响.

Based on Donnell＇ s shallow-shell theory, the wave vibration of a clamped-free rotating thin cylindrical shell subjected to a harmonic load is studied, considering damping and geometric nonlinearity. During the process of investigation, we suppose the thin cylindrical shell is static, while the radial harmonic load moves around circumference at the same speed in the opposite direction. The wave vibration equation is reduced to a coupled system of two nonlinear differential equations with Galerkin method. The numerical solution of the system is obtained through forth-order Runge-Kutta method ,and then the time response and the frequency-amplitude curve of the selected modes are studied. Finally the stability of time response at the resonant frequency and the influence of the load amplitude to the nonlinearity are analyzed.