基于小变形的柔性多体系统运动学分析

Kinematic Analysis of Flexible Ltibody Systems Based on Small Deformations

多体系统中柔性体运动一般分为体参考系的范围运动和变形运动。在多数场合，柔性体的变形运动是较小的，可以用对变形广义坐标线性化的动力学方程描述系统动力学行为。但是，目前通用的一些动力学建模方法用于柔性体动力学建模时，存在过早线性化缺陷，导致最终的动力学方程遗失了一些重要的刚柔耦合项。本文采用非线性变形场描述，计及含有变形广义坐标及其导数的二阶小量项，将这种非线性保留到求出偏（角）速度后，再线性化，建立了柔性多体系统相邻柔性体之间参考坐标系的运动学关系，为进一步建立系统动力学方程提供了理论基础。

The motion of flexible bodies in a multibody system can be represented in manyapplications as a superposition of a large references and small deformations,which allows linearization form of the deformation varianles in the dgnamic eqwations.But the defaults exist in some presesnt modeling methods,which are premature lineareization to the deformation variables,and result from rigid-flexible coupling terms losing in final dynamic equations. In this paper,a deformation field of a body is described by using second non-linear of deformation vaiables,and motion variables ane linearized after parial (angular)velocities are obtained. Kinematic relations between coordinate refevences of two adjecent bodies are develoed,which provides the theortical basis for dynamic modeling of flexible multibody systems.