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Reflection of Plane Waves in a Nonlocal Transversely Isotropic Micropolar Thermoelastic Medium with Temperature-Dependent Properties

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Abstract

Purpose

The present research is aimed to investigate the reflection of time-harmonic plane waves in a nonlocal, transversely isotropic, micropolar thermoelastic half-space with temperature-dependent properties under three-phase-lag (TPL) theory.

Methods

Four coupled plane waves with distinct speeds are identified to travel in the medium. Taking into account appropriate boundary constraints, the reflection phenomena is investigated at the stress free surface of the medium.

Results

The expressions of amplitude ratios and energy ratios for the reflected plane waves are obtained. Numerical computations, performed using MATLAB software, analyze the impacts of micropolar parameter, material anisotropy and generalized thermoelasticity theories (TPL and GN theory of type III), as well as the nonlocal parameter and temperature-dependent properties on the amplitude ratios.

Conclusion

The influence of material anisotropy on phase velocities is explored in detail. The computational results are visualized and interpreted through graphs. Notably, it is confirmed that there is no dissipation of energy during the reflection phenomena.

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References

  1. Biot M (1956) Thermoelasticity and irreversible thermodynamics. J Appl Phys 27:240–253

    Article  MathSciNet  Google Scholar 

  2. Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solid 15:299–309

    Article  Google Scholar 

  3. Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7

    Article  Google Scholar 

  4. Green AE, Naghdi PM (1991) A re-examination of the basic postulates of thermomechanics. Proc R Soc Lond Ser A 432:171–194

    Article  MathSciNet  Google Scholar 

  5. Green AE, Naghdi PM (1992) On undamped heat waves in an elastic solid. J Therm Stress 15:253–264

    Article  MathSciNet  Google Scholar 

  6. Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–208

    Article  MathSciNet  Google Scholar 

  7. Roychoudhuri SK (2007) On a thermoelastic three-phase-lag model. J Therm Stress 30:231–238

    Article  Google Scholar 

  8. Quintanilla R, Racke R (2008) A note on stability in three-phase-lag heat conduction. Int J Heat Mass Transf 51:24–29

    Article  Google Scholar 

  9. Said SM (2016) Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model. J Comp Appl Math 291:142–157

    Article  MathSciNet  Google Scholar 

  10. Biswas S, Mukhopadhyay B, Shaw S (2017) Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model. J Therm Stress 40:403–419

    Article  Google Scholar 

  11. Othman MIA, Abbas IA (2023) 2-D Problem of micropolar thermoelastic rotating medium with eigenvalue approach under the three-phase-lag model. Wave Rand Compl media 33:280–295

    Article  Google Scholar 

  12. Said SM (2015) Deformation of a rotating two-temperature generalized-magneto thermoelastic medium with internal heat source due to hydrostatic initial stress. Meccanica 50:2077–2091. https://doi.org/10.1007/s11012-015-0136-x

    Article  MathSciNet  Google Scholar 

  13. Marin M, Hobiny A, Abbas I (2021) The effects of fractional time derivatives in porothermoelastic materials using finite element method. Math 9:1606. https://doi.org/10.3390/math9141606

    Article  Google Scholar 

  14. Said SM (2022) Fractional derivative heat transfer for rotating modified couple stress magneto-thermoelastic medium with two temperatures. Wave Rand Comp Media 32:1517–1534

    Article  MathSciNet  Google Scholar 

  15. Eringen AC, Suhubi ES (1964) Nonlinear theory of micro-elastic solids I. Int J Eng Sci 2:189–203

    Article  MathSciNet  Google Scholar 

  16. Suhubi ES, Eringen AC (1964) Nonlinear theory of micro-elastic solids II. Int J Eng Sci 2:389–404

    Article  MathSciNet  Google Scholar 

  17. Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15:909–923

    MathSciNet  Google Scholar 

  18. Nowacki W (1966) Couple stresses in the theory of thermoelasticity I. Bull Acad Polon Sci Ser Sci Technol 14:129–138

    Google Scholar 

  19. Nowacki W (1966) Couple stresses in the theory of thermoelasticity II. Bull Acad Polon Sci Ser Sci Technol 14:263–272

    Google Scholar 

  20. Nowacki W (1966) Couple stresses in the theory of thermoelasticity III. Bull Acad Polon Sci Ser Sci Technol 14:801–809

    Google Scholar 

  21. Eringen AC (1970) Foundation of Micropolar Thermoelasticity. Courses and Lectures, CISM, Udine, Vol. 23. Springer, Wien

  22. Eringen AC (1972) Linear theory of nonlocal elasticity and dispersion of plane waves. Int J Eng Sci 10:425–435

    Article  Google Scholar 

  23. Eringen AC (1974) Theory of nonlocal thermoelasticity. Int J Eng Sci 12:1063–1077

    Article  Google Scholar 

  24. Eringen AC (1999) Theory of micropolar elasticity. Microcontinuum field theories I: foundations and solids. Springer, New York, pp 101–248

    Chapter  Google Scholar 

  25. Eringen AC (2002) Nonlocal continuum field theories. Springer, New York

    Google Scholar 

  26. Eringen AC (1984) Plane waves in nonlocal micropolar elasticity. Int J Eng Sci 22:1113–1121

    Article  Google Scholar 

  27. Kumar R, Gupta RR (2010) Propagation of waves in transversely isotropic micropolar generalized thermoelastic half space. Int Commun Heat Mass Transf 37:1452–1458

    Article  Google Scholar 

  28. Abbas IA, Kumar R (2014) Interaction due to a mechanical source in transversely isotropic micropolar media. J Vibr Contr 20:1663–1670

    Article  MathSciNet  Google Scholar 

  29. Challamel N, Grazide C, Picandet V (2016) A nonlocal Fourier’s law and its application to the heat conduction of one-dimensional and two-dimensional thermal lattices. Comptes Rendus Mec 344:388–401

    Article  Google Scholar 

  30. Kalkal KK, Sheoran D, Deswal S (2020) Reflection of plane waves in a nonlocal micropolar thermoelastic medium under the effect of rotation. Acta Mech 231:2849–2866

    Article  MathSciNet  Google Scholar 

  31. Said SM (2020) The effect of mechanical strip load on a magneto-micropolar thermoelastic medium: Comparison of four different theories. Mech Res Comm 107:103549

    Article  Google Scholar 

  32. Marin M, Seadawy A, Vlase S, Chirila A (2022) On mixed problem in thermoelasticity of type III for Cosserat media. J Taib Uni Sci 16:1264–1274

    Article  Google Scholar 

  33. Poonia R, Deswal S, Kalkal KK (2023) Propagation of plane waves in a nonlocal transversely isotropic thermoelastic medium with voids and rotation. Z Angew Math Mech. https://doi.org/10.1002/zamm.202200493

    Article  Google Scholar 

  34. Said SM, Othman MIA (2023) 2D problem of a nonlocal thermoelastic diffusion solid with gravity via three theories. J Vib Eng Technol. https://doi.org/10.1007/s42417-023-01172-4

    Article  Google Scholar 

  35. Said SM (2024) Gravitational influence on a nonlocal thermoelastic solid with a heat source via L-S Theory. J Vib Eng Technol

  36. Barak MS, Poonia R. Devi S, Dhankhar P (2024) Nonlocal and dual-phase-lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids. Z Angew Math Mech. https://doi.org/10.1002/zamm.202300579

  37. Achenbach JD (1973) Wave propagation in elastic solids. North Holland-Elsevier, Amsterdam

    Google Scholar 

  38. Lomakin VA (1976) The theory of elasticity of non-homogeneous bodies. Moscow State University Press, Moscow

    Google Scholar 

  39. Khurana A, Tomar SK (2016) Wave propagation in nonlocal microstretch solid. Appl Math Model 40:5858–5875

    Article  MathSciNet  Google Scholar 

  40. Kumar S, Tomar SK (2021) Reflection of coupled waves from the flat boundary surface of a nonlocal micropolar thermoelastic half-space containing voids. J Therm Stress 44:1191–1220

    Article  Google Scholar 

  41. Ewing WM, Jardetzky WS, Press F (1957) Elastic waves in layered media. McGraw-Hill Book Company, INC, New York

    Book  Google Scholar 

  42. Gupta RR (2014) Reflection of waves in micropolar transversely isotropic thermoelastic half space of GN type II and III. J Mech Behav Mater 23:27–35

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, 125001, India

    Sunita Deswal & Kapil Kumar Kalkal

  2. Department of Mathematics, Government College, Hisar, Haryana, 125001, India

    Priti Dhankhar

  3. Department of Mathematics, Government College, Nalwa (Hisar), Haryana, 125037, India

    Ravinder Poonia

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  1. Sunita Deswal
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  2. Kapil Kumar Kalkal
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  3. Priti Dhankhar
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  4. Ravinder Poonia
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Correspondence to Ravinder Poonia.

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Deswal, S., Kalkal, K.K., Dhankhar, P. et al. Reflection of Plane Waves in a Nonlocal Transversely Isotropic Micropolar Thermoelastic Medium with Temperature-Dependent Properties. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01378-0

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  • DOI: https://doi.org/10.1007/s42417-024-01378-0

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