An application of elastodynamic reciprocity to reflection by an obstacle in a waveguide

J. D. Achenbach

doi:10.1017/S1727719100001660

An application of elastodynamic reciprocity to reflection by an obstacle in a waveguide

J. D. Achenbach^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

Original language	English (US)
Pages (from-to)	97-101
Number of pages	5
Journal	Journal of Mechanics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1017/S1727719100001660
State	Published - 2000
Externally published	Yes

ASJC Scopus subject areas

Condensed Matter Physics
Mechanical Engineering
Applied Mathematics

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title = "An application of elastodynamic reciprocity to reflection by an obstacle in a waveguide",

abstract = "The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.",

author = "Achenbach, {J. D.}",

note = "Funding Information: This work was carried out in the course of research sponsored by the Office of Naval Research under Contract No. N00014-89-J1362.",

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T1 - An application of elastodynamic reciprocity to reflection by an obstacle in a waveguide

AU - Achenbach, J. D.

N1 - Funding Information: This work was carried out in the course of research sponsored by the Office of Naval Research under Contract No. N00014-89-J1362.

PY - 2000

Y1 - 2000

N2 - The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

AB - The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

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An application of elastodynamic reciprocity to reflection by an obstacle in a waveguide

Abstract

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