【摘要】 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。更多还原

【Abstract】 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.更多还原