On damping in two‐layer elastic‐viscoelastic media
Michael Renardy · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2004
Abstract We consider one‐dimensional wave propagation through two layers consisting, respectively, of an elastic and a viscoelastic medium. We show that, if the instantaneous elastic modulus of the viscoelastic medium is infinite, then there exists a family of modes with frequencies going to infinity, but damping rates going to zero. Hence the overall rate of damping is not exponential. On the other hand, there is a possibility of faster than exponential damping (i.e., the damping rate goes to infinity with frequency) if the elastic moduli of the two media are matched and the derivative G′(0) of the relaxation modulus of the viscoelastic medium is ‐∞.