Some One-Dimensional Dynamical Problems

Abstract

We now consider some dynamical problems involving especially simple geometries: torsional oscillations of a rod, and propagation of plane waves in a semi-infinite medium. We have several purposes in mind. First, these problems illustrate some important similarities between the behavior of viscoelastic materials and the behaviors of materials that are purely viscous or purely elastic, and they also illustrate some important distinctions. Second, we wish to illustrate that viscoelasticity problems can be analyzed to significant depth even if the basic response functions are given only graphically or numerically, in the form of data. Third, the mathematical techniques used in these problems are of interest in themselves because they find applications in many areas.