针对奇异二阶系统的解耦问题,提出了一种基于谱变换的解耦方法. 首先分析了质量矩阵非奇异的解耦条件,提出一种非奇异二阶同谱对角系 统的构造解耦方法,然后引入谱变换将首系数转换为非奇异的,利用非奇异的构造方法来构造同谱对角系统,最后对解耦系统进行还原,从而实现奇异二阶系统的解耦. 数值试验证明该方法确实有效.

In order to solve the singular quadratic system decoupling problem, a new method of singular quadratic system decoupling based on spectral  ransformation is proposed in this paper. By analyzing the decoupling condition with nonsingular mass matrix, an explicit construction decoupling is given for quadratic isospectral system with nonsingular leading coefficient. Then a spectral transformation is introduced to transform singular system into nonsingular system, and a nonsingular quadratic system decoupling is used to construct and restore decoupled system, thus realize the decoupling of singular quadratic systemis realized. Finally, a numerical example is presented to prove the availability of the method.