On wave propagation in viscoelastic media

TLDR: In this paper, a mathematical analysis of wave propagation in a one-dimensional bounded viscoelastic medium under prescribed boundary conditions is made, and closed form expressions for wave velocity as a function of ratio of relaxation frequency to frequency of applied periodic displacement are obtained for the steady state part of the solution.

Abstract: A mathematical analysis is made of the problem of wave propagation in a one-dimensional bounded viscoelastic medium under prescribed boundary conditions. Closed form expressions are obtained for viscoelastic waves for the case of a relaxation function involving a single relaxation time. An expression for the phase velocity as a function of ratio of relaxation frequency to frequency of applied periodic displacement is obtained for the steady state part of the solution. The generalization to a relaxation function involving a finite number of relaxation times is discussed, and a method is sketched out for solving the more general integropartial differential equation of motion. Comments are made on the molecular interpretation of viscoelastic models.