柔性多体系统弹性碰撞动力学建模

Dynamic Modeling of a Flexible Multibody System with Elastic Impact

以平面柔性双摆为研究对象,基于Hertz接触理论,考虑几何非线性,用变分原理建立了柔性体的动力学变分方程,根据运动学约束关系,运用缩并法,建立了柔性双摆系统接触碰撞的动力学方程.首先通过柔性单摆和固定刚性物体的撞击实验验证了建模理论的正确性.在此基础上,对柔性双摆系统进行仿真计算,得到了撞击力变化规律,并揭示了横向变形和角速度在冲击波传播过程中的突变现象.

The modeling of a flexible multibody system with elastic impact was investigated. Based on Hertz impact theory, dynamic variational equation of each flexible body was established, in which the geometric nonlinearity is taken into account. By using kinematic constraint equations and reduced coordinate formulation, equations of flexible double pendulum were derived. An experiment of the impact of a flexible pendulum with a fixed rigid body was carried out to verify the correctness of the modeling method, and then a flexible double pendulum was simulated to obtain the time history of the impact force. The result shows the sudden change of angular velocity and the transverse deformation during the course of impact wave propagation.