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RESEARCH PAPERS

Harmonic Waves in Layered Composites: New Bounds on Eigenfrequencies

[+] Author and Article Information
C. O. Horgan

Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Ill. 60201

K.-W. Lang, S. Nemat-Nasser

Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Ill. 60201

J. Appl. Mech 45(4), 829-833 (Dec 01, 1978) (5 pages) doi:10.1115/1.3424427 History: Received January 01, 1978; Revised June 01, 1978; Online July 12, 2010

Abstract

The purpose of this paper is to present new approaches to the problem of wave frequency estimation for harmonic waves in layered elastic composites. Upper and lower bounds are obtained by adapting standard results for eigenvalue problems with smooth coefficients. The one-dimensional eigenvalue problem with discontinuous coefficients of concern here is first transformed by using an analog of the classical Liouville transformation. Upper bounds are obtained by application of a Rayleigh-Ritz technique to the transformed problem. Explicit lower bounds in terms of the coefficients are established. Results are illustrated by numerical examples.

Copyright © 1978 by ASME
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