The study examines the impact of various theories on the reflection and transmission phenomena caused by obliquely incident longitudinal and transverse waves at the interface between a continuously elastic solid half-space and a thermoelastic half-space, using multiple thermoelastic models. Numerical calculations reveal that the thermoelastic medium supports one transmitted transverse wave and two transmitted longitudinal waves. The modulus of amplitude proportions is analyzed as a function of the angle of incidence, showing distinct variations across the studied models. Energy ratios, derived from wave amplitudes under consistent surface boundary conditions for copper, are computed and compared across angles of incidence. The results demonstrate that the total energy ratio consistently sums to one, validating energy conservation principles. Graphical comparisons of amplitude proportions and energy ratios for SV and P waves across different models illustrate significant differences in wave behavior, emphasizing the influence of thermoelastic properties on wave transmission and reflection.

1. McCarthy MF. Wave propagation in generalized thermoelasticity. International Journal of Engineering Science. 1972; 10(7): 593–602.

2. Sharma JN, Sidhu RS. On the propagation of plane harmonic waves in Anisotropic generalized thermoelasticity. International Journal of Engineering Science. 1986; 24(9): 1511–1516.

3. Banerjee DK, Pao YH. Thermoelastic waves in anisotropic solids. The Journal of the Acoustical Society of America. 1974; 56(5): 1444–1454. doi: 10.1121/1.1903463

4. Puri P. Plane waves in generalized thermoelasticity. International Journal of Engineering Science. 1973; 11(7): 735–744.

5. Chadwick P, Seet LTC. Wave propagation in a transversely isotropic heat‐conducting elastic material. Mathematika. 1970; 17(2): 255–274. doi: 10.1112/s002557930000293x

6. Dhaliwal RS, Sherief HH. Generalized thermoelasticity for anisotropic media. Quarterly of Applied Mathematics. 1980; 38(1): 1–8. doi: 10.1090/qam/575828

7. Chandrasekharaiah DS. Wave propagation in a thermoelastic half-space. Indian Journal of Pure and Applied Math. 1981; 12: 226–241.

8. Singh H, Sharma JN. Generalized thermoelastic waves in transversely isotropic media. The Journal of the Acoustical Society of America. 1985; 77(3): 1046–1053. doi: 10.1121/1.392391

9. Sharma MD. Wave Propagation in Anisotropic Generalized Thermoelastic Media. Journal of Thermal Stresses. 2006; 29(7): 629–642. doi: 10.1080/01495730500499100

10. Prasad R, Kumar R, Mukhopadhyay S. Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags. International Journal of Engineering Science. 2010; 48(12): 2028–2043. doi: 10.1016/j.ijengsci.2010.04.011

11. Lykotrafitis G, Georgiadis HG, Brock LM. Three-dimensional thermoelastic wave motions in a half-space under the action of a buried source. International Journal of Solids and Structures. 2001; 38(28–29): 4857–4878.

12. Sharma MD. Wave propagation in a general anisotropic poroelastic medium with anisotropic permeability: phase velocity and attenuation. International Journal of Solids and Structures. 2004; 41(16–17): 4587–4597. doi: 10.1016/j.ijsolstr.2004.02.066

13. Venkatesan M, Ponnusamy P. Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section immersed in a fluid. International Journal of Mechanical Sciences. 2007; 49(6): 741–751. doi: 10.1016/j.ijmecsci.2006.10.003

14. Kumar R, Kansal T. Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. International Journal of Solids and Structures. 2008; 45(22–23): 5890–5913. doi: 10.1016/j.ijsolstr.2008.07.005

15. Yu J, Wu B, He C. Guided thermoelastic wave propagation in layered plates without energy dissipation. Acta Mechanica Solida Sinica. 2011; 24: 135–143.

16. Kumar R, Gupta V. Reflection and transmission of plane waves at the interface of an elastic half-space and a fractional order thermoelastic half-space. Archive of Applied Mechanics. 2013; 83(8): 1109–1128. doi: 10.1007/s00419-013-0737-6

17. Youssef HM, El-Bary AA. Theory of hyperbolic two temperature generalized thermoelasticity. Journal of Material Physics and Mechanics. 2018; 40: 158–171.

18. Lata P, Kaur I, Singh K. Thermomechanical interactions due to time harmonic sources in a transversely isotropic magneto thermoelastic rotating solids in Lord-Shulman model. Journal of Material Physics and Mechanics. 2020; 46: 7–26.

19. Kumar R, Bansal P, Gupta V. Reflection and transmission at the interface of an elastic and two-temperature generalized thermoelastic half-space with fractional order derivative. Journal of Material Physics and Mechanics. 2021; 47: 1–19.

20. Sherief H, Anwar MN, El-Latief AA, et al. A fully coupled system of generalized thermoelastic theory for semiconductor medium. Scientific Reports. 2024; 14(1). doi: 10.1038/s41598-024-63554-2

21. Ding W, Patnaik S, Sidhardh S, Semperlotti F. Displacement-driven approach to nonlocal elasticity. Nanomechanics of Structures and Materials. 2024; 277–317. doi: 10.1016/b978-0-443-21949-8.00016-4

22. Li S, Zheng W, Li L. Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures. International Journal of Mechanical Sciences. 2024; 282: 109572. doi: 10.1016/j.ijmecsci.2024.109572

23. Kumar R, Kaushal S, Kochar A. Analysis of axisymmetric deformation in generalized micropolar thermoelasticity within the framework of Moore-Gibson-Thompson heat equation incorporating non-local and hyperbolic two-temperature effect. The Journal of Strain Analysis for Engineering Design. 2024; 59(3): 153–166. doi: 10.1177/03093247241232180

24. Yadav AK, Carrera E, Marin M, Othman MIA. Reflection of hygrothermal waves in a Nonlocal Theory of coupled thermo-elasticity. Mechanics of Advanced Materials and Structures. 2024; 31(5): 1083–1096. doi: 10.1080/15376494.2022.2130484

25. Abd-Alla AM, Othman MIA, Abo-Dahab SM. Reflection of Plane Waves from Electro-magneto-thermoelastic Half-space with a Dual-Phase-Lag Model. Computers Materials & Continua. 2016; 51(2): 63–79.

26. Othman MIA, Abo-Dahab SM, Alsebaey ONS. Reflection of Plane Waves from a Rotating Magneto-thermoelastic Medium with Two-temperature and Initial Stress under Three Theories. Mechanics and Mechanical Engineering. 2017; 21(2): 217–232.

27. Biot MA. Thermoelasticity and Irreversible Thermodynamics. Journal of Applied Physics. 1956; 27(3): 240–253. doi: 10.1063/1.1722351

28. Lord HW, Shulman Y. A generalized dynamical theory of thermo-elasticity. Journal of Mechanics and Physics of Solids. 1967; 15(5): 299–309.

29. Green AE, Lindsay KA. Thermoelasticity. Journal of Elasticity. 1972; 2(1): 1–7. doi: 10.1007/bf00045689

30. Green AE, Naghdi PM. On undamped heat waves in an elastic solid. Journal of Thermal Stresses. 1992; 15(2): 253–264. doi: 10.1080/01495739208946136

31. Green AE, Naghdi PM. Thermoelasticity without energy dissipation. Journal of Elasticity. 1993; 31(3): 189–208. doi: 10.1007/bf00044969

32. Choudhuri SKR. On a thermoelastic three-phase-lag model. Journal of Thermal Stresses. 2007; 30(3): 231–238. doi: 10.1080/01495730601130919

33. Tzou DY. A unified field approach for heat conduction from macro- to micro-scales. Journal of Heat Transfer. 1995; 117(1): 8–16. doi: 10.1115/1.2822329

34. Kumar R, Kansal T. Reflection and refraction of plane waves at the interface of an elastic solid half-space and a thermoelastic diffusive solid half-space. Archives of Mechanics. 2012; 64: 293–317.

35. Borcherdt RD. Reflection-refraction of general P-and type-I S-waves in elastic and anelastic solids. Geophysical Journal of the Royal Astronomical Society. 1982; 70(3): 621–638. doi: 10.1111/j.1365-246x.1982.tb05976.x

36. Achenbach JD. In: Wave propagation inelastic solids. Elsevier Science Publishers; 1973.

37. Sherief HH, Saleh HA. A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures. 2005; 42(15): 4484–4493. doi: 10.1016/j.ijsolstr.2005.01.001

38. Bullen KE. In: An introduction to the theory of seismology. Cambridge University Press; 1963.