A Correspondence Principle for Free Vibrations of a Viscoelastic Solid

Abstract

A correspondence principle for free vibrations in the classical linearized theory of viscoelasticity is established. It is shown that, for motions which are either irrotational or solenoidal, there is always an associated elastic problem with the following properties: (a) Every mode shape for the viscoelastic problem is also a mode shape for the elastic problem; and (b) the viscoelastic frequencies can, in principle, be calculated from a knowledge of the elastic spectrum and the relevant relaxation function. It is further shown that, in general, for motions which are neither irrotational nor solenoidal, this correspondence exists only for the restricted class of viscoelastic materials for which the behavior depends essentially upon one relaxation function. The paper concludes with the observation that the correspondence also exists for those approximate theories in which there appears only one relaxation function.