刚-柔耦合多体系统动力学建模与数值仿真

柔性多体系统动力学传统的混合坐标建模方法忽略了变形位移的高次耦合变形量，是一种零次近似方法，其适用范围受到限制。本文以中心刚体、柔性粱及末端质量组成的刚柔耦合系统为对象，考虑了有粘性阻尼及风阻的情况。在柔性粱的纵向变形位移中计及了横向位移引起的轴向变形，并采用有限元方法和Hamilton变分原理导出了系统的刚柔耦合一次近似的动力学方程。该方程充分计及了中心刚体的大范围运动与柔性粱的弹性变形运动的相互耦合，并采用一致的方法引入了阻尼因素。文中最后提供了一个比“动力刚化”问题更具有一般性的仿真计算反例，进一步说明了零次近似方法在处理某些刚一柔耦合动力学问题时的缺陷，同时表明了由一次近似模型可得到正确合理的结论。

Dynamics modeling and numerical simulation for a rigid-flexible coup ling multibody system

The traditional hybrid coordinate model of flexible m ultibody system is considered as a zero order approximate dynamic model due to its neglect of the high order coupling deformation kinematics. This a pproach fails to account for dynamic stiffening and may lead to erroneous re sults in some high speed cases. This paper presents a finite element model for a multibody system consisting of a rotating hub and a flexible beam with a tip m ass. The corresponding dynamics models of the viscous damping and air resistance are developed in a consistent manner. Based on the deformation theory and geome tric constraints, the longitudinal deformation due to the transverse deflection is t aken into account and the effect of dynamic stiffening is captured. This mod el is different from the model for dynamic stiffening problem in that the la rge overall motion of the reference frame of the beam is not prescribed and is a ffected by elastic deformation. A numerical example is given in the end, which i s more general than the well know n example for dynamic stiffening. This example illustrates not only the defic iency of the zero order approximate dynamic model more profoundly, but also the validity of the proposed model.