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On Love-type waves in a finitely deformed magnetoelastic layered half-space

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Abstract

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney–Rivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein–Gulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK

    Prashant Saxena

  2. School of Engineering, University of Aberdeen King’s College, Aberdeen, AB24 3UE, UK

    Ray W. Ogden

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  1. Prashant Saxena
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  2. Ray W. Ogden
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Correspondence to Prashant Saxena.

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Saxena, P., Ogden, R.W. On Love-type waves in a finitely deformed magnetoelastic layered half-space. Z. Angew. Math. Phys. 63, 1177–1200 (2012). https://doi.org/10.1007/s00033-012-0204-1

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