考虑几何非线性的旋转薄壁圆柱壳进动响应分析

Precession response analysis of thin rotating circular cylindrical shell considering geometric nonlinearity

选取悬臂旋转薄壁圆柱壳作为研究对象,利用能量法推导了其振型进动因子,并考虑了阻尼以及几何非线性的影响。应用Donnell’s简化壳理论建立考虑几何非线性以及振型进动的非线性波动方程,使用Galerkin法对非线性波动方程进行离散化,获得模态坐标上的非线性微分方程组,分别应用Runge-Kutta法和谐波平衡法对其进行数值求解和近似解析求解,并分析了近似解析解的稳定性。结果表明,几何非线性不影响振型进动因子,但使系统的频率响应曲线具有多值性和跳跃性。

A cantilever thin rotating circular cylindrical shell is investigated in this paper. The precession factor of vibrating shape is obtained by an energy approach, with damping and geometric nonlinearity considered. Donnell＇s shallow-shell theory is used, the non-linear equations of motion are discretized by Galerkin method, in which geometric nonlinearity and precession of vibrating shape are taken into account. The non-linear mode equations are studied by using Runge-Kutta method and harmonic balance method, and the stability of analytical solutions is studied. The results show that geometric nonlinearity does not influence the precession factor of vibrating shape but causes multi-value and leap characteristics.