 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13088 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8125
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| In English (Mech. Solids): | | 4963 |
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| Srijit Goswami, Nantu Sarkar, and Marin Marin, "Thermoelastic Wave Propagation in the Moore–Gibson–Thompson Theory," Mech. Solids. 60 (1), 776-793 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
1 |
Pages |
776-793 |
| DOI |
10.1134/S0025654425600230 |
| Title |
Thermoelastic Wave Propagation in the Moore–Gibson–Thompson Theory |
| Author(s) |
Srijit Goswami (Department of Applied Mathematics, University of Calcutta, Kolkata, 700 009 India)
Nantu Sarkar (Department of Applied Mathematics, University of Calcutta, Kolkata, 700 009 India)
Marin Marin (Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, 500036 Romania; Academy of Romanian Scientists, Bucharest, 050045 Romania, marin@unitbv.ro) |
| Abstract |
This manuscript investigates harmonic plane wave propagation in a time differential
Moore–Gibson–Thompson thermoelastic medium. It is noted that six possible plane harmonic waves may propagate at different speeds. Among these, two are transverse waves, while the other four
are coupled longitudinal waves. The transverse waves are decoupled, undamped over time, and propagate independently at a speed unaffected by the thermal field. The four longitudinal plane waves
exhibit coupling, temporal damping, and dispersion due to the thermal influence of the medium.
A longitudinally quasi-elastic wave decays exponentially over time, with its amplitude diminishing to
zero as time progresses toward infinity. A stationary quasi-thermal wave also decays exponentially to
zero over time. Additionally, there are two possible dilatational quasi-thermal propagating waves with
varying rates of time damping, or there could be a single time-harmonic dilatational thermal wave,
depending on the time delay value. The problem of surface waves is also discussed for Moore–Gibson–Thompson thermoelasticity. The surface of the half-space is assumed to be traction-free and able
to exchange heat freely with the surrounding medium. The dispersion relation for the surface wave is
explicitly formulated, and the secular equation is derived. Numerical simulations are carried out for
both plane and surface waves within a specified model. The computed results are visually depicted,
and a summary analysis of these outcomes is provided. |
| Keywords |
MGT thermoelasticity, time harmonic plane waves, surface waves, secular equation, minimal dispersion |
| Received |
18 January 2025 | Revised |
30 January 2025 | Accepted |
31 January 2025 |
| Link to Fulltext |
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