Wave propagation according to the linearized finite theory of elasticity

This paper completely solves the problem of wave propagation in constrained linear elastic materials within the framework of the linearized finite theory of elasticity proposed by Hoger and Johnson in 1995. By means of a procedure of linearization appropriate for such a theory, in a previuos paper we have derived the amplitude condition. In this paper we obtain the acoustic tensor and the propagation condition solving an eigenvalue problem related to this tensor. Moreover, we solve with the right degree of accuracy the characteristic equation. In general, our results differ by terms which are first order in the displacement gradient from the corresponding results obtained in the classical linear elasticity, as explicitly shown by the study of the constraints of incompressibility and inextensibility.