COMPUTATION OF EIGENVALUES AND EIGENVECTORS OF NONCLASSICALLY DAMPED SYSTEMS

Conventionally, the eigenanalysis of a nonclassically damped dynamic s ystem is performed in a space of twice the system's dimension. This an d the properties of the matrices characterizing the system in this spa ce make the analysis costly, particularly for large systems. Prior to the development several years ago by Cronin of a new computational met hod, there was no alternative to the conventional analysis. The conver gence of the new method was not established then by Cronin, but he ill ustrated it by analyzing a number of representative systems. We set ou t 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 r igorous and useful convergence condition. The revised method for eigen analysis is derived here, as is its convergence condition. Illustrativ e worked examples are included, notably an example involving a gyrosco pic system that illustrates the utility of the method for the case of a non-symmetric damping matrix.