构造多自由度无阻尼系统微分方程的一种方法

A Method of Constructing Differential Equation Coefficient Matrix in Undamped MDOF System

针对多自由度无阻尼线性定常系统,根据系统的动能、势能与运动方程决定的动能、势能分别相等的原理,提出构造微分方程系数矩阵方法,现有的直接法,视察法是此方法的特例。此方法的优点是:在建立运动微分方程的过程中,没有对时间求导的过程,也没有对方程整理和简化的过程;既适用于单自由度系统又适用于多自由度系统;既适用于手工建模又方便于计算机建模。在该方法的基础上,又论述了运动微分方程解耦的数学条件,为广义坐标的选取明确了方向。

There are many methods for mathematical modeling in the undamped MDOF linear constant system , but these methods are often limited by either the usage condition or fussy calculations,and not suitable to computer modeling.According to the principle of the system's kinetic energy,potential energy and the equal principle of kinetic energy and potential energy by the moving equation,the matrix method of constructing differential equation system was put forward.The direct approach and inspection method are the specific cases.The advantage of this method is that there are no processes of solving differential coeffient for time and of settling and simplifying the equation in establishing the moving differential equation.This method is suitable to both single degree of freedom and multiple degrees of freedom system. It is also applicable to the handicraft modeling and convenient for computer modeling.Based on the method,the mathematical conditions of moving differential equation decoupling are exporunded for the selection of the broad sense coordinate.