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Reflection of thermoelastic plane waves at a stress-free insulated solid boundary with memory-dependent derivative

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Abstract

In the present manuscript, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermoelastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material. The Lord–Shulman model under the heat transfer law with memory-dependent derivative is employed to model this problem. The case of total reflection is taken into account to calculate the critical angle. Phase velocities and corresponding attenuation factors of the coupled dilatational elastic-thermal waves and the ratios of the reflection coefficients are calculated and illustrated graphically for copper-like material and highlighted the effects of various parameters of interest.

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Acknowledgements

The authors would like to gratefully acknowledge the Editor and the reviewers for their constructive and valuable comments and suggestions to improve the quality of the manuscript.

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The authors received no financial support for the research.

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Authors and Affiliations

  1. Department of Mathematics, City College, Kolkata, 700009, India

    Nihar Sarkar

  2. Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, India

    Soumen De

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  1. Nihar Sarkar
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  2. Soumen De
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Correspondence to Soumen De.

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Sarkar, N., De, S. Reflection of thermoelastic plane waves at a stress-free insulated solid boundary with memory-dependent derivative. Indian J Phys 95, 1203–1211 (2021). https://doi.org/10.1007/s12648-020-01788-2

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  • DOI: https://doi.org/10.1007/s12648-020-01788-2

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