A Theorem for Non-existence of Composite Exceptional Waves in Anisotropic Elastic Materials Due to Dimensional Considerations

Abstract

In the theory of elastic waves in anisotropic materials the transonic states have been ordered into 6 types, labeled type 1 to type 6. For the type 6 case it has been shown that the three partial waves involved always will form a composite exceptional wave. When the transonic wave problem can be reduced to two dimensions the equivalent transonic state will be of type 4. In the present paper it is shown that in this case the two partial waves will never form a composite exceptional wave, thus limiting the equivalence because of the dimensionality of the problem.