Reflection of plane waves from the boundary of an incompressible finitely deformed electroactive half-space

Singh, B. and Ogden, R. W. (2018) Reflection of plane waves from the boundary of an incompressible finitely deformed electroactive half-space. Zeitschrift für Angewandte Mathematik und Physik, 69, 149. (doi: 10.1007/s00033-018-1044-4)

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Abstract

Within the framework of the quasi-electrostatic approximation, the theory of the superposition of infinitesimal deformations and electric fields on a finite deformation with an underlying electric field is employed to examine the problem of the reflection of small amplitude homogeneous electroelastic plane waves from the boundary of an incompressible finitely deformed electroactive half-space. The theory is applied to the case of two-dimensional incremental motions and electric fields with an underlying biassing electric field normal to the half-space boundary, and the general incremental governing equations are obtained for this specialization. For illustration, the equations are then applied to a simple prototype electroelastic model for which it is found that only a single reflected wave is possible and a surface wave is in general generated for each angle of incidence. Explicit formulas are obtained for the wave speed and the reflection and surface wave coefficients in terms of the deformation, magnitude of the electric (displacement) field, the electromechanical coupling parameters, and the angle of incidence, and the results are illustrated graphically.

Item Type:Articles
Additional Information:The work of Dr. Baljeet Singh was supported by a grant under the bilateral agreement between the Royal Society of Edinburgh and the Indian National Science Academy for his visit to Glasgow.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond and Singh, Dr Baljeet
Authors: Singh, B., and Ogden, R. W.
College/School:College of Science and Engineering > School of Mathematics and Statistics
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Zeitschrift für Angewandte Mathematik und Physik
Publisher:Springer
ISSN:0044-2275
ISSN (Online):1420-9039
Published Online:12 November 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Zeitschrift für Angewandte Mathematik und Physik 69: 149
Publisher Policy:Reproduced under a Creative Commons License

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