The reflection of planewaves in a generalized microstretch thermoelastic medium considering initial stress and two temperature effects
*Jiten SharmaCorresponding authorjitensharma1922@gmail.comDepartment of MathematicsChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Sangeeta Kumarisangwan.sangeeta.ss@gmail.comDepartment of MathematicsChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2641
- Pages:
- 2553–2564
Abstract
The propagation of plane waves in a two-dimensional microstretch thermoelastic medium with two temperatures and initial stress is examined in this study. The study makes use of microstretch theory, which incorporates two temperature considerations, rotation, microstretch effects, and initial stress at the microscale. The Coupled Transverse Displacement (CTD) wave, the Coupled Microrotational Displacement (CMD) wave, and three other waves---the Coupled Longitudinal Displacement (CLD) wave, the Coupled Thermal (CT) wave, and the Coupled Transverse Microrotational (CTM) wave---are found when the model’s basic equations are solved for the plane waves. Using the proper boundary conditions, for the five waves the reflection coefficients are calculated, and the graphical results are displayed.
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References
[1] R. B. Hetnarski and J. Ignaczak, “Generalized thermoelasticity,” J. Therm. Stresses, vol. 22, no. 4-5, pp. 451-476 (1999), doi: 10.1080/014957399280832.
[2] M. A. Biot, “The influence of initial stress on elastic waves,” J. Appl. Phys., vol. 11, no. 8, pp. 522-530 (1940), doi: 10.1063/1.1712807.
[3] S. Tang, “Wave propagation in initially-stressed elastic solids,” Acta Mech., vol. 4, no. 1, pp. 92-106 (1967), doi: 10.1007/BF01291091.
[4] S. Dey and S. K. Addy, “Reflection of plane waves under initial stresses at a free surface,” Int. J. Non-Linear Mech., vol. 12, no. 6, pp. 371-381 (1977).
[5] R. W. Ogden and D. A. Sotiropoulos, “The effect of pre-stress on the propagation and reflection of plane waves in incompressible elastic solids,” IMA J. Appl. Math., vol. 59, no. 1, pp. 95-121 (1997), doi: 10.1093/imamat/59.1.95.
[6] M. I. A. Othman and Y. Song, “Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation,” Int. J. Solids Struct., vol. 44, no. 17, pp. 5651-5664 (2007), doi: 10.1016/j.ijsolstr.2007.01.022.
[7] J. Sharma, S. Kumari, and S. Sharma, “Reflection of plane waves with two temperature and initial stress in nonlocal thermo elasticity without energy dissipation,” Grenze Int. J. Eng. Technol., vol. 10 (2024).
[8] S. Kumari, M. Singh, and S. Sharma, “Influence of gravity and hydrostatic initial stress on wave propagation in context of three phase lag thermoelasticity,” Mech. Solids, vol. 59, no. 4, pp. 1990-2009 (2024), doi: 10.1134/S0025654424602921.
[9] E. C. Bingham, “Plasticity and elasticity,” J. Franklin Inst., vol. 197, no. 1, pp. 99-115 (1924).
[10] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity. Cambridge, U.K.: Cambridge University Press (1927).
[11] A. C. Eringen, “Microstretch elasticity,” in Microcontinuum Field Theories: I. Foundations and Solids. New York, USA: Springer, pp. 249-267 (1999).
[12] B. Singh and R. Kumar, “Wave propagation in a generalized thermo-microstretch elastic solid,” Int. J. Eng. Sci., vol. 36, no. 7-8, pp. 891-912 (1998), doi: 10.1016/S0020-7225(97)00099-2.
[13] Y. Q. Song, M. I. A. Othman, and Z. Zhao, “Reflection of plane waves from a thermo-microstretch elastic solid with temperature dependent elastic properties,” Multidiscip. Model. Mater. Struct., vol. 10, no. 2, pp. 228-249 (2014), doi: 10.1108/MMMS-07-2013-0052.
[14] M. I. A. Othman, E. E. M. Eraki, and M. F. Ismail, “A comparative study of temperature-dependent characteristics and non-local behavior in a submerged microstretch thermoelastic medium using two models,” Sci. Rep., vol. 14, p. 27096 (2024), doi: 10.1038/s41598-024-77233-9.
[15] M. Kaur, R. Kumar, S. Sharma, H. H. Taha, A. Kamel, A. A. El-Bary, and K. Lotfy, “Two temperatures effect on wave propagation in microstretch thermoelastic medium with microtemperatures,” Sci. Rep., vol. 15, p. 43816 (2025), doi: 10.1038/s41598-025-31454-8.
[16] S. Kumar, H. Nagar, and S. Kumari, “Surface waves in hygro-thermoelastic half-space with hydrostatic initial stress, rotation & magnetic field,” J. Interdiscip. Math., vol. 29, no. 6, pp. 2049-2065 (2026), doi: 10.47974/JIM-2583.
[17] S. Kumari, Bharti, and B. Singh, “Effects of two-temperature on Rayleigh wave in generalized magneto-thermoelastic media with hydrostatic initial stress,” J. Heat Transfer, vol. 141, no. 7, p. 072002 (2019), doi: 10.1115/1.4043677.
[18] P. Ailawalia, Priyanka, M. Marin, and H. Altenbach, “Variable thermal conductivity in context of Green-Naghdi theory of thermo-microstretch solids,” ZAMM - J. Appl. Math. Mech., vol. 104, no. 4, p. e202400010 (2024), doi: 10.1002/zamm.202400010.
[19] V. A. Eremeyev, L. P. Lebedev, and H. Altenbach, Foundations of Micropolar Mechanics. Berlin, Germany: Springer (2012), doi: 10.1007/978-3-642-28353-6.
[20] H. von Helmholtz, “Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen,” J. Reine Angew. Math., vol. 55, pp. 25-55 (1858), doi: 10.1515/crll.1858.55.25.
[21] B. Singh, A. K. Yadav, and D. Gupta, “Reflection of plane waves from a micropolar thermoelastic solid half-space with impedance boundary conditions,” J. Ocean Eng. Sci., vol. 4, no. 2, pp. 122-131 (2019), doi: 10.1016/j.joes.2019.02.003.
[22] S. Kumari, M. Singh, and S. Sharma, “Gravitational effect on piezo-thermoelasticity in the context of three phase lag model with two temperature,” Int. J. Appl. Comput. Math., vol. 9, no. 6, p. 139 (2023), doi: 10.1007/s40819-023-01617-0.
[23] B. Singh, “Propagation characteristics of plane waves in nonlocal isotropic diffusive materials,” Appl. Math. Model., vol. 104, pp. 306-314 (2022), doi: 10.1016/j.apm.2021.11.028.
[24] M. I. A. Othman, S. Y. Atwa, A. Jahangir, and A. Khan, “Gravitational effect on plane waves in generalized thermo-microstretch elastic solid under Green Naghdi theory,” Appl. Math. Inf. Sci. Lett., vol. 1, no. 2, pp. 25-38 (2013).




