Wave propagation in viscoelastic media

The mathematical formulations of the wave propagation problem in a linear viscoelastic solid are reviewed from the point of view of constitutive equations and the theory of linear physical systems. Various general results from the theory of propagating singular surfaces and from the mathematical theory of hyperbolic equations are applied to the analysis of the wave propagation process. The impulse response of three viscoelastic media are analyzed by use of asymptotic methods. The three material models are the standard linear solid, the standard linear solid with a continuous spectrum of relaxation times, and the power law solid.