Radial Vibrations of Media with Spherical Interfaces

Abstract

Statement and solution of problems on radial (centrally symmetric) vibrations of the elastic media with spherical interfaces (internal boundaries) can be considered to be a particular case of axially symmetric problems, which we analyze in Chap. 3. Nevertheless, it is useful to study the problems on radial vibrations preliminarily, before making analysis of the more general cases. This can be explained, first, from a historical point of view, since the studies of different problems of dynamics of elastic spherical bodies, as a rule, were always started by the studies of radial vibrations. Secondly, an opportunity to derive the sufficiently simple solutions of the centrally symmetric problems allows us to reveal some useful qualitative effects that take place in the more general cases. Physically, a main simplification consists in the absence of shear waves; mathematically, the number of unknown functions is lower.