柔性梁斜碰撞问题的非线性动力学建模和实验研究

Nonlinear Dynamic Modeling and Experiment Investigation for a Flexible Beam with Oblique Impact

本文研究柔性梁点面斜碰撞问题。用Hertz接触模型处理法向撞击力,分别用Hertz切向接触模型和Coulomb摩擦力模型处理粘滞状态和滑动状态的摩擦力。从精确的应变与位移的关系出发,用绝对节点坐标法建立了柔性梁的动力学方程。为了准确地处理斜碰撞切向运动的复杂状态,提出滑动-粘滞切换的准则,在此基础上,设计了斜碰撞实验,数值对比了法向撞击力和法向速度的时间历程的仿真计算结果与实验结果,验证了Hertz理论在斜碰撞情况下的正确性。另一方面切向速度的实验与理论的结果对照表明滑动-粘滞切换准则的有效性。

An oblique impact between a flexible rectangular beam and a fixed rigid sphere body was investigated. Hertz contact model was used to deal with normal impact force, and Hertz tangential contact model and Coulomb friction model were used to deal with static tangential impact force and slip frictional force, respectively. Based on the exact relation between strain and displacement, the impact dynamic equations were established by the absolute nodal co-ordimate formulation. In order to solve the complicated oblique impact problem, the stick slip friction phenomenon was analyzed by establishing transition criteria that predict the transition between the stick and slip states of interface, and then, the experiment technique of oblique contact was introduced. The time histories of normal impact force and normal velocity were tested and calculated, respectively. The agreement of the experiment and simulation results verified the correctness of the use of Hertz impact model in oblique impact problem. Furthermore, the time history of tangential velocity was tested and calculated, respectively, which shows that the criteria for the transition between the stick and slip states can be effectively used for solving tangential impact problem.