考虑附加质量的旋转柔性梁的随机动力学分析

Stochastic dynamic analysis of rotating flexible beam with tip mass

研究了带有附加质量的旋转柔性梁系统在参数具有随机性时的动力响应问题。基于假设模态法和Lagrange方程建立了带有附加质量的柔性悬臂梁系统的一次近似耦合随机动力学方程,利用混沌多项式结合高效回归法将其转化为完全隐式纯微分方程,求解方程得到柔性悬臂梁变形响应的数字特征。最后,通过数值仿真对物理参数和几何参数具有随机性的系统进行动力特性研究。仿真结果表明:利用随机参数的动力学模型能客观地反映出系统的动力学行为;部分随机参数的分散性对柔性体动力响应的影响不可忽视。

Dynamic response of rotating flexible beam with tip mass and uncertain parameters is investigated.Based on assumed modes method and Lagrange′s equations,the first-order approximation coupling stochastic dynamic equations are derived.The polynomial chaos method and a regression-based collocation method are applied to derive system of completely implicit differential equations.The resulting system of equations is then used to find the numerical characteristics of the response.As an illustrating example,dynamic modeling of flexible hub-beam system considering probabilistic geometric and physical parameters is presented.Simulation results demonstrate that probabilistic parameters have effect on the dynamic response of the flexible beam,and the dynamic modeling with probabilistic parameters can objectively reflect the actual dynamic response of flexible system.