Modal Identities for Elastic Bodies, With Application to Vehicle Dynamics and Control

Abstract

It is a standard procedure to analyze a flexible vehicle in terms of its vibration frequencies and mode shapes. However, the entire mode shape is not needed per se, but two integrals of the mode shape, pi and hi , which correspond to the momentum and angular momentum in Mode i. Together with the natural frequencies ωi , these modal parameters satisfy several important identities, 25 of which are derived in this paper. Expansions in terms of both “constrained” and “unconstrained” modes are considered. A simple illustrative example is included. The paper concludes with some remarks on the theoretical and practical utility of these results, and several potential extensions to the theory are suggested.