Coupled Rayleigh surface waves in slowly varying elastic waveguide

Folguera, Alejandra; Harris, John G.

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https://hdl.handle.net/2142/112573 Copy

Description

Title

Coupled Rayleigh surface waves in slowly varying elastic waveguide

Author(s)

• Folguera, Alejandra
• Harris, John G.

Issue Date

1997-10

Keyword(s)

• Rayleigh Surface Waves
• Elastic Waveguide

Abstract

A combination of the two lowest Rayleigh-Lamb modes can approximate, on one surface, a Rayleigh surface wave for a waveguide of uniform thickness with traction-free surfaces. The waves are inplane, linearly elastic. The guide is one or more shear wavelengths thick. However, because the guide is not infinitely thick, the Rayleigh wave is weakly coupled to the opposite surface and will transfer to that surface and then back over a distance of several wavelengths. A mathematical framework is developed to understand this process in a waveguide whose thickness changes slowly with respect to wavelength. Using as a small parameter the variation in thickness over a wavelength, an asymptotic expansion, that represents the lateral propagation with rays, but the transverse variation with local Rayleigh-Lamb modes, is used. In adapting this expansion to in plane elastic wave propagation, we reformulate the problem for the Rayleigh-Lamb modes as an eigenvalue problem whose eigenvector is comprised of the two displacement components and the two components of the traction acting on a plane perpendicular to the guide's axis. This enables us to exploit the orthogonality between the modes given by the reciprocity relation. The zeroth order analysis indicates that, for waveguides with increasing thickness, the coupling phenomenon endures indefinitely (in the absence of damping) if the rate of growth of the thickness is at most logarithmic. For a waveguide whose thickness varies only slowly, sinusoidally, the coupling persists more or less as it would in a uniform guide.

Publisher

Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign

Series/Report Name or Number

• TAM R 868
• 1997-6029

ISSN

0073-5264

Type of Resource

text

Language

eng

Permalink

http://hdl.handle.net/2142/112573

Sponsor(s)/Grant Number(s)

National Science Foundation 97/10 29555 AC 9 97/10; Air Force Office of Scientific Research 97/10 DMS 95 00723 97/10; Petroleum Research Fund 97/10 F 49620 96 1 0190 97/10

Copyright and License Information

Copyright 1997 Board of Trustees of the University of Illinois

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