Applying Eigenvalue Perturbation Theory to Solve Problems in Structural Dynamics

Abstract

In this paper the eigenvalue perturbation theory is applied to solve various problems in structural dynamics. Detailed derivations are presented along with examples to demonstrate the utility of the approach and its accuracy. In undergraduate classes on mechanical vibration, the eigenvalue perturbation theory is rarely taught, but it can be extremely valuable. The approach can be used to analyze the effects of design changes on the modes of vibration of a dynamical system, to determine the approximate eigensolutions of a nearly uniform continuous system, and to obtain the approximate complex eigencharacteristics of a lightly damped system. This paper shows that the eigenvalue perturbation theory can be easily introduced at the undergraduate level, because to understand the derivations only a first course in linear algebra is required, well within the capability of an undergraduate engineering student.