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Abstract

In this manuscript, we investigate the propagation of plane time-harmonic waves in an infinite linear thermoelastic medium, assuming a known wavelength. For the thermodynamic response, we adopt the Lord–Shulman (L-S) theory of generalized thermoelasticity. Our analysis reveals two uncoupled, undamped transverse waves, along with possibly two to three coupled, temporally damped, and dispersive longitudinal waves. The speed of transverse waves remains unaffected by thermal effects, whereas longitudinal waves exhibit thermal dependence. Indeed, we observe a time-damped longitudinal quasi-elastic wave, with its amplitude exponentially decreasing to zero as time approaches infinity. Furthermore, there may be two possible longitudinal quasi-thermal waves that are damped in time with different decreasing rates or a single plane harmonic in time longitudinal quasi-thermal wave. We also examine surface wave propagation in a semi-infinite thermoelastic medium, considering a stress-free, heat-exchanging half-space boundary. The explicit forms of the dispersion relation and the secular equation are derived. Numerical computations for both plane and surface waves are conducted using a specific model, with graphical representations of the results and corresponding analytical discussions. Finally, we present generalized observations regarding the surface wave profile.

Keywords

Thermoelasticity time-harmonic plane wave surface wave secular equation minimal dispersion

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References

Duhamel

. Some memoire sur les phenomena thermo-mecanique. J Ecole Polytechn 1885; 15: 1–15.

Neumann

. Vorlesungen über die theorie der elasticität. Breslau: Meyer, 1885.

Biot

. Thermo-elasticity and irreversible thermo-dynamics. J Appl Phys 1956; 27: 249–253.

Lord

Shulman

. A generalized dynamical theory of thermo-elasticity. J Mech Phys Solids 1967; 15: 299–309.

Ulbrich

. Exact electric analogy to the Vernotte hypothesis. Phys Rev 1961; 123: 2001–2002.

Nayfeh

Nemat-Nasser

. Thermoelastic waves in solids with thermal relaxation. Acta Mech 1971; 12: 53–69.

Sinha

. Reflection of thermoelastic waves at a solid half-space with thermal relaxation. Phys Earth Planet Inter 1974; 22: 237–244.

Sharma

Kumar

Chand

. Reflection of generalized thermoelastic waves from the boundary of half space. J Therm Stresses 2003; 26: 925–942.

Singh

Kumar

Singh

. Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress. Appl Math Comput 2006; 177: 170–177.

10.

Singh

. Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space. Appl Math Comput 2008; 198: 494–505.

11.

Othman

MIA

Song

. Reflection of magneto-thermo-elastic waves from a rotating elastic half-space in generalized thermoelasticity under three theories. Mech Eng 2011; 15: 5–24.

12.

Abo-Dahab

Mohamed

Singh

. Rotation and magnetic field effects on p wave reflection from a stress-free surface of elastic half-space with voids under one thermal relaxation time. JVC 2011; 17: 1827–1839.

13.

Das

Sarkar

. Plane waves in nonlocal generalized thermoelasticity. ZAMM 2022; 102: e202000294.

14.

Das

Sarkar

. Reflection of temperature rate-dependent coupled thermoelastic waves on a non-local elastic half-space. Math Mech Solids 2023; 28(5): 1232–1254.

15.

Das

Sarkar

. Plane waves in Moore-Gibson-Thompson thermoelasticity considering nonlocal elasticity effect. Math Mech Solids 2023; 28(9): 1978–1998.

16.

Sarkar

. Reflection phenomena of thermoelastic plane waves on a rigid surface within a size-dependent elastic media. Math Mech Solids. Epub ahead of print 14 November 2024. DOI: 10.1177/10812865221145737.

17.

Achenbach

. Wave propagation in elastic solids. New York: North-Holland, 1976.

18.

Rayleigh

. On waves propagated along the plane surface of an elastic solid. Proc London Math Soc 1885; 17: 4–11.

19.

Chadwick

Windle

. Propagation of Rayleigh waves along isothermal and insulated boundaries. Proc R Soc London A 1964; 280: 47–71.

20.

Tomita

Shindo

. Rayleigh waves in magneto-thermoelastic solids with thermal relaxation. Int J Eng Sci 1979; 17: 227–232.

21.

Ivanov

. On the propagation of thermoelastic Rayleigh waves. Wave Motion 1988; 10: 73–82.

22.

Lockett

. Effect of the thermal properties of a solid on the velocity of Rayleigh waves. J Mech Phys Solids 1958; 7: 71–75.

23.

Deresiewicz

. The effect of boundaries on wave propagation in a liquid-filled porous solid. J Acoust Soc Am 1957; 29: 204–209.

24.

Chakraborty

Pal

. Study of the propagation characteristics of seismic waves. Pure Appl Geophys 1969; 76: 79–86.

25.

Dwan

Chakraborty

. On Rayleigh waves in Green-Lindsay model of generalized thermoelastic medium. Indian J Pure Appl Math 1988; 20: 276–283.

26.

Sharma

Othman

MIA

. Effect of rotation on generalized thermo-viscoelastic Rayleigh lamb waves. Int J Solids Struct 2007; 44: 4243–4255.

27.

Abouelregal

. Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model. Int J Eng Sci 2011; 49: 781–791.

28.

Abd-alla

AAN

Al-Dawy

. Thermal relaxation times effect on Rayleigh waves in generalized thermoelastic media. J Therm Stresses 2001; 24: 367–382.

29.

Singh

. Propagation of Rayleigh wave in a two-temperature generalized thermoelastic solid half-space. ISRN Geophysics. Epub ahead of print 12 February 2013. DOI: 10.1155/2013/857937.

30.

Abo-Dahab

. Surface waves in coupled and generalized thermoelasticity. In: Hetnarski

(ed.) Encyclopedia of thermal stresses. Dordrecht: Springer, 2014, p. 4764–4774.

31.

Kumar

Gupta

. Rayleigh waves in generalized thermoelastic medium with mass diffusion. Can J Phys 2015; 93: 1039–1049.

32.

Ghatuary

Chakraborty

. Thermomagnetic effect on the propagation of Rayleigh waves in an isotropic homogeneous elastic half-space under initial stress. Cogent Eng 2015; 2: 1026539.

33.

Singh

Verma

. On propagation of Rayleigh type surface wave in five different theories of thermoelasticity. Int J Appl Mech Eng 2019; 24: 661–673.

34.

Hou

Carcione

, et al. Simulation of wave propagation based on the Lord-Shulman thermoelastic theory. Geophysics 2021; 86: 155–164.

35.

Chiriţă

Ciarletta

Tibullo

. On the wave propagation in the time differential dual-phase-lag thermoelastic model. Proc R Soc A 2015; 471: 20150400.

36.

Lebeau

Zuazua

. Decay rates for the three-dimensional linear systems of thermoelasticity. Arch Ration Mech Anal 1999; 148: 179–231.

Wave propagation in thermoelastic media with relaxation time

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