Dispersion dependence for Rayleigh‐like vibrations in a low‐density channel

Abstract

Although it is in principle possible to compute dispersion curves for a buried low‐density channel by numerical means, the interpretation of such results is fraught with uncertainty relating to numerical approximations, inaccuracies, and a poorly developed theoretical framework for Rayleigh waves. It is thus interesting to investigate by analytical techniques some simple cases. One of these is a study of the Rayleigh wave in an idealization of a low‐density channel. Such a channel has at least two stationary vibration points and numerous modes with complex wave number as well as the usual four propagating Rayleigh modes. The stationary points are interesting because they correspond to resonant vibrations in an unbounded medium. The algebra required to investigate even this idealized case of a layer bounded above and below by high‐density plates and overlying an elastic half‐space is tedious. It can be automated quite effectively with Mathematica. This algebraic manipulation program also provides simple effective graphics tools to study the qualitative behavior of the results.