Modal Parameter Analysis of Gyroelastic Continua

Abstract

This paper builds on the theory of gyroelastic dynamics presented in a recent paper by the authors. An elastic continuum with a continuous distribution of stored angular momentum ( called gyricity) is considered. We introduce the modal parameters (coefficients) thereof, including integrals of the mode shapes, and show they must satisfy a number of useful identities. In addition to the coefficients (p α and h α ) associated with momentum and angular momentum which also arise in the dynamics of a purely elastic body, there is a third coefficient (g α ) wholly attributable to the gyricity distribution. The modal parameter analysis presented here is an extension of that for purely elastic continua. The analysis concludes with a simple demonstration of the theoretical results using a spatially discretized model of a cantilevered rod.