On the modal analysis of non-conservative linear systems

This paper applies the results of classical eigenvalue theory to the analysis of a non-conservative vibratory system. General results are obtained for the response of a multiple degree-of-freedom system which is represented by a set of linear second-order differential equations with constant coefficients. For the case when the eigenvalues of the system are distinct, these results confirm those obtained by [1]Fawzy and Bishop by a different method. The latter results are restricted to distinct eigenvalues, but the more general analysis presented here allows the case of multiple eigenvalues to be included. The physical interpretation of complex normal co-ordinate vectors is discussed and some simple numerical examples illustrate the results. The approach described here lends itself to numerical computation using computer library programs for eigenvalue determination.