带集中质量的旋转柔性曲梁动力学特性分析

本文对带集中质量的平面内旋转柔性曲梁动力学特性进行了研究.基于绝对节点坐标法推导出曲梁单元,其中该曲梁单元采用Green-Lagrangian应变,并根据曲梁变形前后的曲率变化和曲率的精确表达式计算了曲梁单元弹性力所作的虚功.通过虚功原理,利用$\delta$函数和中心刚体与悬臂曲梁之间的固支边界条件,建立了带集中质量的旋转柔性曲梁非线性动力学模型.基于该模型,本文仿真计算了悬臂曲梁的纯弯曲问题和带有刚柔耦合效应的旋转柔性曲梁动力学响应问题,以此分别讨论了所提出曲梁单元的收敛性和动力学模型的正确性.进一步应用D'Alembert原理,将旋转曲梁等效为带离心力的无旋转曲梁,通过线性摄动处理得到系统的特征方程,以此分别研究了旋转角速度、初始曲率和集中质量对曲梁动力学特性的影响.最后重点分析了旋转曲梁的频率转向和振型切换问题,并阐述了两者之间的相互关系.研究结果表明:随着旋转角速度的增大,曲梁的频率特性与直梁的频率特性相近,以及曲梁拉伸变形占主导的模态振型会提前. 

DYNAMIC CHARACTERISTICS ANALYSIS OF A ROTATING FLEXIBLE CURVED BEAM WITH A CONCENTRATED MASS 1)

The dynamic characteristics of a planar rotating flexible curved beam with a concentrated mass are studied in this paper. The curved beam element is derived based on the absolute nodal coordinate formulation. The element adopts the Green-Lagrangian strain, and the virtual work of the elastic force of the curved beam element is calculated according to the curvature change before and after the deformation of the curved beam and the exact expression of the curvature. Through the virtual work principle, the nonlinear dynamic model of rotating flexible curved beam with a concentrated mass is established by using the $\delta $ function and the fixed boundary condition between the hub and the cantilever curved beam. Based on this model, the pure bending problem of cantilever curved beam and the dynamic response of rotating flexible curved beam with rigid-flexible coupling effect are simulated. According to the results, the convergence of the proposed element and the correctness of the dynamic model are discussed, respectively. Furthermore, applying the D'Alembert principle, the rotating curved beam is equivalent to a non-rotating curved beam with centrifugal forces, and the characteristic equations of the system are obtained by linear perturbation processing. The effects of rotating angular velocity, initial curvature and concentrated mass on the dynamic characteristics of the curved beam are studied, respectively. Finally, the frequency loci veering and mode shift of the rotating curved beam are analyzed, and the interrelation between them is expounded. The results show that with the increase of rotation angular velocity, the frequency characteristics of curved beams are similar to straight beams, and the mode shapes of curved beams dominated by tensile deformation will be advanced.