On the Existence of Type-6 Transonic States in Linear Elastic Media of Cubic Symmetry

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S_1) indeed exist and are the rule, rather than the exception, in so-called C_3 cubic media (satisfying the inequalities c₁₂ + c₄₄ > c₁₁ - c₄₄ > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C_3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids, pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.