基于Riccati传递矩阵法的线性树形多体系统特征值求解

Computation of eigenvalues of linear tree multibody system based on Riccati transfer matrix method

为了提高多体系统传递矩阵法求解线性树形多体系统特征值时的数值稳定性,研究了基于Riccati变换的线性树形多体系统特征值求解方法。建立了元件输入输出端的Riccati传递矩阵递推关系;从树形系统各输入端开始沿传递路径依次求得了各元件联接端的Riccati传递矩阵,并建立了用Riccati传递矩阵表示的系统特征方程;建立了消除系统特征方程极点的方法,从而可以增大求解特征方程时的搜索步长。数值算例计算结果与有限元法计算结果对比验证了该文方法的正确性,与通常多体系统传递矩阵法计算结果对比表明了本文方法具有较高的数值稳定性。

In order to improve the numerical stability in computing the eigenvalues of linear tree multibody systems in the context of transfer matrix method for multibody system（ MSTMM）,the eigenvalue solving strategy of linear tree multibody systems is studied based on the Riccati transformation. The recursive relations of the Riccati transfer matrices between the input and the output ends of elements is established. Starting from each input end of a tree system,the Riccati transfer matrices of the connection ends of each element are obtained along the transfer path successively. The characteristic equation of the system expressed by Riccati transfer matrix is derived. The searching step can be increased when solving the characteristic equation by proposing a technique to eliminate the poles of the characteristic equation. The proposed method is verified by comparing the results of the numerical example with the results of the finite element method（ FEM）. And it also proves that theproposed method has better numerical stability relative to the normal MSTMM.