IJPAM: Volume 40, No. 1 (2007)

WAVE PROPAGATION ACCORDING TO
THE LINEARIZED FINITE THEORY OF ELASTICITY

Maria Luisa Tonon
Department of Mathematics
University of Turin
Via Carlo Alberto 10, Turin, 10123, ITALY
e-mail: marialuisa.tonon@unito.it


Abstract.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 et al [#!2!#], [#!3!#]. By means of a procedure of linearization appropriate for such a theory, in [#!4!#] 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.

Received: September 17, 2007

AMS Subject Classification: 74J30, 74B99

Key Words and Phrases: wave propagation, constrained elastic materials, linearized finite elasticity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1