模态空间系统动态特性分析的一种新方法

A New Method for System Dynamic Characteristics Analysis in the Modal Space

推出了一种分析大干扰下系统动态特性的新方法———模式串(modal series)方法。和向量场正则型变换方法一样,这种方法也是通过2阶解析解来研究系统的内部非线性结构特性,进而达到认识和理解系统动态特性和稳定性的目的。但该方法推导出的2阶解析解不用求取高维非线性代数方程,而且把谐振情况和非谐振情况的公式融为一体推导容易计算简单。在2解解析解的基础上推导出了系统非线性相关因子的表达式。算例结果验证了本文推出的2阶解析解及2阶非线性相关因子的正确性和有效性。

A new algorithm called modal series method is presented for analyzing the system dynamics performance and stability under large disturbance in this paper. The second order analytic solution from the algorithm is used to research the system inner nonlinear structure characteristic, thus the system dynamics performance and stability can he realized and understood as the normal forms theory of vector fields did. But the second order analytic solution may be got without computing the high dimension nonlinear algorithm equation which is an extremely difficult computable work. On the other side the resonance and nonresonance condition are all included in the same solution. Therefore the algorithm is simple and easy to use. On the basis of the second order analytic solution, the foundations of nonlinear participation factors are got. A computing example shows the correctness of the second order analytic solution and the foundation of nonlinear participation factors.