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Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

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Abstract

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia

    Abo-el-nour Abd-alla

  2. Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy

    Ivan Giorgio & Dionisio Del Vescovo

  3. International Research Center for the Mathematics and Mechanics of Complex Systems (MeMoCS), Cisterna di Latina, Italy

    Ivan Giorgio, Luca Galantucci & Dionisio Del Vescovo

  4. Department of Mathematics, Faculty of Science, Sohag University, Sohâg, Egypt

    Abdelmonam M. Hamdan

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  1. Abo-el-nour Abd-alla
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  2. Ivan Giorgio
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  5. Dionisio Del Vescovo
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Correspondence to Ivan Giorgio.

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Communicated by Victor Eremeyev, Peter Schiavone and Francesco dell'Isola.

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Abd-alla, Aen., Giorgio, I., Galantucci, L. et al. Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity. Continuum Mech. Thermodyn. 28, 67–84 (2016). https://doi.org/10.1007/s00161-014-0400-7

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