作大范围运动弹性梁的动力刚化分析

Dynamics of an elastic beam in large overall motion

刚体大范围运动与弹性梁的变形运动的相互耦合将产生动力刚化现象，在经典的动力学理论中无法解释这种现象。本文给出了该系统的运动描述方法，利用Ｈａｍｉｌｔｏｎ变分原理建立了动力学控制方程，利用Ｇａｒｌｅｒｋｉｎ模态截断研究了产生动力刚化的原因及其动力学性质，从本质上解释了学者们多年来一直在研究的动力硬化现象，最后用数值模拟验证了理论的正确性。本文所得结论有益于柔性多体系统动力学的发展。

An elastic beam undergoing the large overall motion will produce dynamic stiffening due to the coupling betwecn rigid motion and elastic deflection. Traditional dynamic methods can not explain these phenomena. The motion description of this system is presented in this paper. According to Hamiltons principle, the dynamic equations of such system is established. The problem of dynamic stiffening is solved from its character through analysis the dynamics of an elastic beam attached to a rigid in large rotation. At last, the digital simulation testify the theory and lots beneficial results are obtained which will benefit the development of dynamics of flexible multi body.