COMPUTATION OF EIGENVALUES AND EIGENVECTORS OF NONCLASSICALLY DAMPED SYSTEMS

Conventionally, the eigenanalysis of a nonclassically damped dynamic system is performed in a space of twice the system's dimension. This and the properties of the matrices characterizing the system in this space make the analysis costly, particularly for large systems. Prior to the development several years ago by Cronin of a new computational method, there was no alternative to the conventional analysis. The convergence of the new method was not established then by Cronin, but he illustrated it by analyzing a number of representative systems. We set out in a present work to develop a predictor of convergence for the new method, and observed that a subtle revision of the method leads to a rigorous and useful convergence condition. The revised method for eigenanalysis is derived here, as is its convergence condition. Illustrative worked examples are included, notably an example involving a gyroscopic system that illustrates the utility of the method for the case of a non-symmetric damping matrix.