精确运动弹性动力学分析方法的显式表达

Explicit Expression for Precise Kineto-elastodynamic Analysis

该文从柔性体的虚位移原理出发,建立精确运动弹性动力分析方法(Kineto ElastodynamicAnalysis)的一种新表达,其运动方程计入刚体大运动与弹性变形的非线性耦合项,整体坐标系下的单元运动方程采用显式表达,避免了在方程中采用旋转变换矩阵的导数,且方程形式及系统方程的组装方式都与基于瞬时结构假设的一般运动弹性动力分析方法保持相同,只需在一般运动弹性动力分析方程中添加几项便可得到该文方程。最后,给出平面连杆机构系统的详细表达。

From the principle of the virtual displacement of a flexible body, a new equation for kineto-elastodynamic analysis is developed. It takes into account the nonlinear coupling effects between the gross motion and the elastic deformation. The element equation is explicitly expressed with global variables. It does not contain the time derivative of the transformation matrix. Meanwhile, it has the same form as the general kineto-elastodynamic analysis which is based on the assumption of the instantaneous structure, and the assembly of the system equations is the same too. The general kineto-elastodynamic analysis equation can be directly developed into the new one just by adding several terms. A particularized expression is developed for the analysis of planar link mechanism, and an example is given to illustrate it at last.