Eigenvalue and Eigenvector Determination for Nonclassically Damped Dynamic Systems

A perturbation method for the eigenanalysis of nonclassically damped dynamic systems is derived and discussed. The method appears to be suitable for the rapid determination to any accuracy of one or all of a system\u27s complex eigenvalue-eigenvector pairs. Although the present study assumes that the system damping matrix is symmetric, this is not required. Thus, the method is suitable for the eigenanalysis of gyroscopic and other interesting systems. The derivation of the method involves a partial diagonalization of the homogeneous equations of motion by the eigenvectors of the undamped system. A perturbation quantity based on the off-diagonal terms of the partially diagonalized damping matrix is defined. The eigenvalues and eigenvectors for the damped system are described in terms of power series in the perturbation quantity. Equations are developed for the general coefficient in each power series. The potential value of the method is illustrated by the eigenanalysis of a set of example systems. For the majority of the systems analyzed, the method produced results in less time than the standard Foss approach