A multi-constrained elastic wave problem

Abstract

It is well known that when an elastic body is subject to N internal constraints (3- N) plane waves propagate in all but certain exceptional directions. The fact that when N ⩾ 3 waves propagate only in these exceptional directions seems to have precluded detailed analysis of multi-constrained wave propagation problems. Recently, however, a model for A-15 superconductors near cubic-tetragonal phase transformations involves the use of four internal constraints. In this paper the propagation of plane waves in elastic bodies subject to these four internal constraints is discussed. To elucidate the form of the slowness surface three of the constraints are relaxed and the singularities occurring on the multi-constrained slowness surface are then explained. The paper concludes with a brief consideration of the direction of energy propagation.