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由于弹性体与刚体之间的动力耦合，使得耦合多体系统的特征值问题非自共轭，难以用经典的模态分析方法解决含有刚、弹耦合多体系统的动力响应问题。本文以某多体系统为例，建立了耦合多体系统的特征值和边值问题的增广公式，进而求得了用正交的增广特征矢量级数表示的系统对任意激励的响应。
Due to the dynamic coupling between elastomer and rigid body, the eigenvalue problem of coupled multi-body system is not self-conjugate, and it is difficult to solve the dynamic response problem of rigid body and elastic coupled multi-body system by classical modal analysis. In this paper, a multi-body system is taken as an example to establish the augmented formulas for the eigenvalues and boundary value problems of coupled multi-body systems, and then the response of the system to arbitrary stimuli with orthogonal augmented eigenvector series is obtained.