刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系,牵连坐标系,物体坐标系及单元坐标系组成,实现了对刚体平动,刚体转动及弹性运动的连续分解,最大限度地消除了由于刚体大角度转动导致的非线性特性。以有限元法为基础,应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程。该方程具有耦合程度小、易于推导、编程及求解等优点,为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了平面铰链约束的约束形式及约束方程,最后给出了一个典型多体系统的数值算例。

Dynamic Analysis of Constrained Multibody Systems with Coupled Rigid and Flexible Motion

In this paper a new kind of coordinate system for describing multibody systems is presented , which realises a complete resolution of rigid translation, rigid orientation and elastic vibration, so that the couplings between rigid motions and elastic deformations are greatly reduced. Based on Lagrange's equation and finite element method, the equations of complex spatial constrained multibody systems are established under the new coordinate system. The equations of planar constraints and the numerical method of dynamic equations are also discussed. A numerical example is given in this paper.