一般复矩阵特征根和特征矢量求解及运用

Eigenvalue and Eigenvector Solutions of a General Complex Matrix and Its Simulating Application

颤振方程在频率内的求解方法是通过状态方程中实矩阵的特征根和特征矢量求解来完成的。通过直接求解颤振方程中的复矩阵来计算颤振频率和颤振速度的,同时详细推导了一般复矩阵的特征根和特征矢量的计算过程。最后利用复矩阵求解特征根和特征矢量的原理,用P-K法解决了颤振方程中颤振问题。

Flutter equations in frequency domain, is solved by using of solutions of eigenvalues and eigenvectors of a real matrix in a state-space form. However, in this paper a general complex matrix from the flutter equation is used to compute directly the flutter frequencies and flutter speeds. Furthermore, the eigenvalues and eigenvectors of a gener- al complex matrix are derived in detail. Finally, according to the solving principle of eigenvalues and eigenvectors of a general complex matrix, a practical flutter problem is solved through P-K method.