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On the Wave Propagation in the Thermoelasticity Theory with Two Temperatures

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Abstract

This paper considers the thermoelastic theory with two temperatures that involves higher gradients of thermal and mechanical effects. The wave propagation question is addressed within the class of waves of assigned wavelength. Considering harmonic in time wave solutions, it is found that the transverse waves are undamped in time and non-dispersive, and they are not altered by the thermal effects. Conversely, the longitudinal waves are dispersive and damped in time; the dispersion relation is established like a cubic equation and the effects of conductive temperature are explicitly presented. Rayleigh surface waves are also studied and an explicit secular equation is derived by using wave solutions damped in time. Illustrative examples are numerically analyzed and graphically depicted. The results achieved are meaningful because they are able to bring information about the propagation of waves with assigned length and, moreover, they are in agreement with the results regarding the wave speed of travelling discontinuities. Also the structure of the wave solutions provides information upon asymptotic stability.

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Acknowledgements

The authors thank the reviewers for their careful reading of our manuscript and their many insightful comments and useful suggestions.

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Authors and Affiliations

  1. University of Salerno, via Giovanni Paolo II n. 132, 84084, Fisciano, Italy

    Ciro D’Apice & Vittorio Zampoli

  2. Department of Mathematics, Alexandru Ioan Cuza University, Bulevardul Carol I n. 11, 700506, Iaşi, Romania

    Stan Chiriţă

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  1. Ciro D’Apice
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  2. Vittorio Zampoli
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  3. Stan Chiriţă
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Correspondence to Stan Chiriţă.

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D’Apice, C., Zampoli, V. & Chiriţă, S. On the Wave Propagation in the Thermoelasticity Theory with Two Temperatures. J Elast 140, 257–272 (2020). https://doi.org/10.1007/s10659-020-09770-z

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