基于刚体运动与弹性运动的机械系统动力学建模研究

DYNAMICS MODELING ANALYSIS OF THE MECHANISM SYSTEM BASED ON RIGID BODY MOTION AND ELASTIC MOTION

讨论了具有刚体运动与柔性变形的机械系统的动力学建模．将刚体自由度与弹性变形自由度看作广 义坐标，利用有限元法对具有刚性运动与弹性变形的机械系统的运动与变形进行了描述，得到了以刚体位 移与弹性变形位移表示的单元的广义惯性力；从应力应变入手，得到了表示单元弹性变形与几何非线性变 形的结构刚度矩阵与几何非线性刚度矩阵，使用 Kane 方程推导了弹性连杆机构的单元运动方程．这种建模 方法，可以使用在任意结构的机械系统．

The dynamics modeling of the mechanical system with flexible deformation and rigid body motion was discussed. Regarding the rigid body motion degree of freedom and the elastic deformation degree of freedom as the generalized coordinate, and using the finite element method to describe the motion and deformation of the elastic connecting rod with elastic deformation and rigid body motion, we obtained the generalized inertial force in terms of the rigid body displacement and the elastic deformation displacement, Considering the relationship of the stress-strain, we also obtained the structural stiffness matrix,which represents the elastic deformation,and the geometric non-linear stiffness matrix, which represents the nonlinear deformation of the deformed body, Using the Kane equation, we derived the movement equation of the elastic connecting rod organization. This kind of modeling method can be used in the mechanical system with arbitrary structure.