Abstract
This study investigates the thermo-mechanical behavior of generalized thermoelastic mediums under the influence of gravitational fields, incorporating two-temperature effects through the Lord–Shulman and dual-phase-lag models. Focusing on a plane surface subjected to an arbitrary normal force and maintained at isothermal conditions, analytical expressions for conductive temperature, thermodynamic temperature, displacement components, and force stresses are derived using normal mode analysis. Numerical results, presented graphically, consider the application of thermal force. Comparative analyses between the dual-phase-lag and Lord-Shulman models are conducted, examining the impact of gravity and the two-temperature effect. Engineering applications of these findings can enhance the understanding of thermal management in materials subjected to varying gravitational environments, such as aerospace structures and thermal barrier coatings.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11043-024-09712-5/MediaObjects/11043_2024_9712_Fig12_HTML.png)
Similar content being viewed by others
Data availability
No datasets were generated or analysed during the current study.
References
Abo-Dahab, S.M., El-Bary, A.A., Al-Hadeethi, Y., Alkashif, M.: Mathematical model on gravitational electro-magneto-thermoelasticity with two temperature and initial stress in the context of three theories. Mathematics 8(5), 735 (2020)
Abouelregal, A.E., Zenkour, A.M.: Generalized thermoelastic interactions due to an inclined load at a two-temperature half-space. J. Theor. Appl. Mech. 54, 827–838 (2016)
Biot, M.A.: Mechanics of Incremental Deformation, pp. 273–281. Willy, New York (1965)
Bromwich, T.J.: On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe. Proc. Lond. Math. Soc. 30, 98–120 (1898)
Chandrasekharaiah, D.S.: Thermoelasticity with second sound. Appl. Mech. Rev. 39, 354–376 (1986)
Chen, P.J., Gurtin, M.E.: On a theory of heat conduction involving two-temperatures. J. Appl. Math. Phys. 19, 614–627 (1968)
Chen, P.J., Gurtin, M.E., Willams, W.O.: On the thermodynamics of non-simple elastic material with two temperatures. Z. Angew. Math. Phys. 20, 107–112 (1969)
De, S.N., Sengurta, P.R.: Surface waves under the influence of gravity. Gerl. Beitr. Geophys. (Leipzig) 85, 311–318 (1976)
Eraki, E.E.M., Fathy, R.A., Othman, M.I.A.: Thomson effect on an initially stressed diffusive magneto-thermoelastic medium via dual-phase-lag model. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-023-01261-4
Lord, H.W., Shulman, Y.A.: Generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
Mandal, S., Sarkar, S.P., Roy, T.K.: An investigation on two temperature dual-phase-lag model of thermoelasticity under fuzzy environment. Int. J. Appl. Comput. Math. 5, 166 (2019)
Mittal, G., Kulkarni, V.S.: Dual-phase-lag thermoelastic problem in a finite cylindrical domain with relaxation time. Multidiscip. Model. Mater. Struct. 14, 837–856 (2018)
Othman, M.I.A.: Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time. Acta Mech. 169, 37–51 (2004)
Othman, M.I.A., Atwa, S.Y., Eraki, E.E.M., Ismail, M.F.: A thermoelastic micro-elongated layer under the effect of gravity in the context of the dual-phase lag model. J. Appl. Math. Mech. 101, e202100109 (2021). https://doi.org/10.1002/zamm.202100109
Othman, M.I.A., Atwa, S.Y., Eraki, E.E.M., Ismail, F.M.: The effect of rotation on thermoelastic microelongated medium under DPL model. J. Appl. Math. Comput. 7(1), 1–14 (2023)
Othman, M.I.A., Eraki, E.E.M., Ismail, M.F.: Study of micro-elongated thermoelastic medium loaded with a piezoelectric layer under the influence of gravity using the dual-phase-lag model. Int. J. Mech. Syst. Dyn. 3, 136–145 (2023)
Quintanilla, R., Jordan, P.: A note on the two temperature theory with dual-phase-lag delay: some exact solutions. Mech. Res. Commun. 36(7), 796–803 (2009)
Sarkar, N.: Analysis of magneto-thermoelastic response in a fiber-reinforced elastic solid due to hydrostatic initial stress and gravity field. J. Therm. Stresses 37, 387–404 (2014)
Sarkar, N., Lahiri, A.: Eigenvalue approach to two-temperature magneto-thermoelasticity. Vietnam J. Math. 40(1), 13–30 (2012)
Sarkar, N., Lahiri, A.: The effect of gravity field on the plane waves in a fiber-reinforced two-temperature magneto-thermoelastic medium under Lord-Shulman theory. J. Therm. Stresses 36, 895–914 (2013)
Sarkar, N., Mondal, S.: Thermoelastic interactions in a slim strip due to a moving heat source under dual-phase-lag heat transfer. J. Heat Transf. 141(12), 124501 (2019) (7 pages)
Sarkar, N., Mondal, S.: Thermoelastic plane waves under the modified Green-Lindsay model with two-temperature formulation. J. Appl. Math. Mech. 100(11), e201900267 (2020)
Sarkar, N., Abo-Dahab, S.M., Mondal, S.: Reflection of magneto-thermoelastic waves at a solid half-space under modified Green-Lindsay model with two temperatures. J. Therm. Stresses 43(9), 1083–1099 (2020)
Sharma, D.K., Thakur, P., Sarkar, N.: Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with void. Mech. Based Des. Struct. Mach. 50(11), 3949–3965 (2022)
Sheokand, S.K., Kalkal, K.K., Deswal, S.: Thermoelastic interactions in a functionally graded material with gravity and rotation under dual-phase-lag heat conduction. Mech. Based Des. Struct. Mach. 51, 3026–3045 (2020)
Thakur, B., Kumari, S., Kumar, A.: Rayleigh wave propagation with rotation, two temperature with diffusion in context to dual phase lag thermoelasticity. Commun. Math. Appl. 14(3), 1215–1228 (2023)
Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9, 686–693 (1995a)
Tzou, D.Y.: A unified field approach for heat conduction from macro to microscales. J. Heat Transf. 117, 8–16 (1995b)
Tzou, D.Y.: Macro-to Microscale Heat Transfer: The Lagging Behavior, p. 576. Wiley, New York (2014)
Warren, W.E., Chen, P.J.: Wave propagation in the two temperature theory of thermoelasticity. Acta Mech. 16, 21–23 (1973)
Youssef, H.: Theory of two-temperature generalized thermoelasticity. IMA J. Appl. Math. 71(3), 383–390 (2006)
Acknowledgements
The authors would like to gratefully acknowledge the Editor and the unknown reviewers’ for their constructive and valuable comments and suggestions to improve the quality of the manuscript.
Funding
The authors received no financial support for the research.
Author information
Authors and Affiliations
Contributions
N.S. completed the whole manuscript himself.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sarkar, N. Thermo-mechanical interaction in two-temperature time-differential dual-phase-lagging materials under gravitational field influence. Mech Time-Depend Mater (2024). https://doi.org/10.1007/s11043-024-09712-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11043-024-09712-5