刚弹耦合多体系统增广特征矢量及其正交性

Augmented Eigenvector of Multibody System Coupled with Rigid and Elastic Bodies and Its Orthogonality

特征矢量的正交性是用模态方法求解多体系统动力响应的前提条件。对于刚弹耦合多体系统,振型函数不具有通常意义下的正交性。本文引入了多体系统增广特征矢量的概念,解决了多体系统特征矢量的正交性问题。系统地阐述了多体系统增广特征矢量的构造方法、正交性条件、正交性证明以及增广特征矢量的重要作用。利用增广特征矢量的正交性,可实现对多体系统动力学方程的坐标解耦,使得用模态方法精确分析动力响应成为可能。

In multibody system dynamics, the orthogonality of eigenvector is the precondition to solve the dynamic response of system using the classical modal analysis methods. For a multibody system coupled with rigid and elastic bodies, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new conception-augmented eigenvector was introduced, and by means of which the orthogonality problem of eigenvectors of multibody system was overcome. The constitution method, the orthogonality condition and the orthogonality proving for augmented eigenvector and its importance were expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in. dynamics equations can be released, which makes it possible to analyze exactly the dynamic response of multibody system using the classical modal analysis method.