The propagation of small amplitude nonlinear waves in a strongly inhomogeneous medium-Reference-Cited by-同舟云学术

The propagation of small amplitude nonlinear waves in a strongly inhomogeneous medium

Published:2011-02-21 Issue:6 Volume:16 Page:637-651
ISSN:1081-2865
Container-title:Mathematics and Mechanics of Solids
language:en
Short-container-title:Mathematics and Mechanics of Solids

Author:

Mortell Michael P¹,Seymour Brian R²

Affiliation:

1. Department of Applied Mathematics, University College, Cork, Ireland

2. Department of Mathematics, University of British Columbia, Vancouver, Canada,

Abstract

A small amplitude wave is propagated into a semi-infinite, strongly inhomogeneous, nonlinear elastic material. The inhomogeneity is chosen, as in functionally graded materials, so that a closed form exact solution is possible within linear theory. The relationship with the approximate solution described by geometrical acoustics, when the inhomogeneity is slowly varying, is readily seen. The nonlinear result is derived by adjusting the linear characteristic as in Whitham’s nonlinearization technique. Shocks may then occur.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Link

http://journals.sagepub.com/doi/pdf/10.1177/1081286510387849

Reference6 articles.

1. Geometrical Theory of Diffraction*

2. Lewis, RM The progressing wave formalism. In: Proceedings of the Symposium on Quasi-Optics, Polytechnic Institute of Brooklyn, 1964, pp. 71-103.

3. Nonlinear Geometrical Acoustics

4. Bleustein–Gulyaev waves in some functionally graded materials

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