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Wave propagation with two delay times in an isotropic porous micropolar thermoelastic material

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Abstract

In this paper, we are following the plane time-harmonic waves propagation in an entire linear thermoelastic space, knowing the wavelength. Concerning the thermodynamic response, we fit the dual phase-lag model, while the effect of porosity on elasticity is given by Cowin–Nunziato theory. We obtain two shear waves and five longitudinal waves as: quasi-elastic wave, quasi-microrotational wave quasi-micropolar wave, quasi thermal mode, quasi-phase-lag thermal mode. The purpose of numerical simulations and of graphs is to identify the influence of connection between thermoelasticity, microrotation and porosity.

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References

  1. Eringen, A.C.: Linear theory of micropolar elasticity. J. Math. Mech. 15, 909–923 (1966)

    MathSciNet  Google Scholar 

  2. Eringen, A.C.: Theory of micropolar elasticity. In: Fracture (Edited by H. Leibowitz), Vol II, Academic Press, New York, 622 (1968)

  3. Eringen, A.C.:Theory of Micropolar Elasticity. In: Microcontinuum Field Theories. Springer, New York (1999)

  4. Passarella, F.: Some results In micropolar thermoelasticity. Mech. Res. Commun. 23(4), 349–357 (1996)

    Article  MathSciNet  Google Scholar 

  5. Ciarletta, M., Svanadze, M., Buonanno, L.: Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids. Eur. J. Mech. A. Solids 28(4), 897–903 (2009)

    Article  MathSciNet  Google Scholar 

  6. Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983)

    Article  Google Scholar 

  7. Nowacki, W.: The Linear Theory of Micropolar Elasticity. CISM International Centre for Mechanical Sciences, 1–43 (1974)

  8. Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995)

    Article  Google Scholar 

  9. Tzou, D.Y.: Macro- to Microscale Heat Transfer: The Lagging Behavior, 2nd edn. Wiley, Chichester (2014)

    Book  Google Scholar 

  10. Jiang, S., Racke, R.: Evolution Equations in Thermoelasticity, Chapman and Hall/CRC,Boca Raton (2000)

  11. Gurtin, M.E.: Variational principles for linear elastodynamics. Arch. Ration. Mech. Anal. 16(1), 34–50 (1964)

    Article  MathSciNet  Google Scholar 

  12. Fabrizio, M., Lazzari, B.: Stability and second law of thermodynamics in dual-phase-lag heat conduction. Int. J. Heat Mass Transf. 74, 484–489 (2014)

    Article  Google Scholar 

  13. Singh, S.S., Lianngenga, R.: Effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids. Appl. Math. Model. 49 (2017)

  14. Chadwick, P., Seet, L.T.C.: Wave propagation in a transversely isotropic heat-conducting elastic material. Mathematika 17(2), 255–274 (1970)

    Article  MathSciNet  Google Scholar 

  15. Kumar, R., Gupta, V.: Effect of phase-lags on Rayleigh wave propagation in thermoelastic medium with mass diffusion. Multidiscip. Model. Mater. Struct. 11(4), 474–493 (2015)

    Article  Google Scholar 

  16. Sharma, S., Kumari, S., Singh, M.: Rayleigh wave propagation in two-temperature dual phase lag model with impedance boundary conditions. Adv. Math.: Sci. J. 9(9), 7525–7534 (2020)

    Google Scholar 

  17. Yadav, A.K.: Thermoelastic waves in a fractional-order initially stressed micropolar diffusive porous medium. J. Ocean Eng. Sci. 6(4), 376–388 (2021)

    Article  Google Scholar 

  18. Gauthier, R.D.: Experimental investigation on micropolar media. Mechanics of Micropolar Media, pp. 395–463 (1982)

  19. Othman, M.I.A., Fekry, M., Marin, M.: Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating. Struct. Eng. Mech. 73(6), 621–629 (2020)

    Google Scholar 

  20. Marin, M., Seadawy, A., Vlase, S., Chirila, A.: On mixed problem in thermos-elasticity of type III for Cosserat media. J. Taibah Univ. Sci. 16(1), 1264–1274 (2020)

    Article  Google Scholar 

  21. Codarcea-Munteanu, L., Marin, M., Vlase, S.: The study of vibrations in the context of porous micropolar media thermoelasticity and the absence of energy dissipation. J. Comput. Appl. Mech. 54(3), 437–454 (2023)

    Google Scholar 

  22. Scutaru, M.L., Vlase, S., Marin, M.: Symmetrical mechanical system properties-based forced vibration analysis. J. Comput. Appl. Mech. 54(4), 501–514 (2023)

    Google Scholar 

  23. Vlase, S., Marin, M., Elkhalfi, A., Ailawalia, P.: Mathematical model for dynamic analysis of internal combustion engines. J. Comput. Appl. Mech. 54(4), 607–622 (2023)

    Google Scholar 

  24. Marin, M., Hobiny, A. Abbas, I.: The effects of fractional time derivatives in porothermoelastic materials using finite element method. Mathematics, 9(14), Art. No. 1606 (2021)

  25. Abbas, I., Hobiny, A., Marin, M.: Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity. J. Taibah Univ. Sci. 14(1), 1369–1376 (2020)

    Article  Google Scholar 

  26. Marin, M., Fudulu, I.M., Vlase, S.: On some qualitative results in thermodynamics of Cosserat bodies, Boundary Value Problems 2022, Art. No. 69 (2022)

  27. Marin, M., Vlase, S., Fudulu, I.M., Precup, G.: Effect of voids and internal state variables in elasticity of porous bodies with dipolar structure. Mathematics 9(21), Art. No. 2741 (2021)

  28. Marin, M., Vlase, S., Fudulu, I.M., Precup, G.: On instability in the theory of dipolar bodies with two-temperatures. Carpathian J. Math. 38(2), 459–468 (2022)

    Article  MathSciNet  Google Scholar 

  29. Bhatti, M.M., Marin, M., Ellahi, R., Fudulu, I.M.: Insight into the dynamics of EMHD hybrid nanofluid (ZnO/CuO-SA) flow through a pipe for geothermal energy applications. J. Thermal Anal. Calorimetry 148(96) (2023)

  30. Fudulu, M.: Plane strain of isotropic micropolar bodies with pores. Bulletin of the Transilvania University of Brasov Series III Mathematics and Computer Science (2023)

  31. Marin, M., Öchsner, A.: The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity. Continuum Mech. Thermodyn. 29(6), 1365–1374 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. Marin, M., Öchsner, A.: Essentials of Partial Differential Equations. Springer, Cham (2018)

    Google Scholar 

  33. Bhatti, M.M., Anwar Bég, O., Kuharat, S.: Electromagnetohydrodynamic (EMHD) convective transport of a reactive dissipative carreau fluid with thermal ignition in a non-Darcian vertical duct. Numer. Heat Transf. (2023)

  34. Bhatti, M.M., Ellahi, R.: Numerical investigation of non-Darcian nanofluid flow across a stretchy elastic medium with velocity and thermal slips. Numer. Heat Transf. Part B: Fundam. 83(5), 323–343 (2023)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036, Brasov, Romania

    D. M. Neagu, I. M. Fudulu & M. Marin

  2. Academy of Romanian Scientists, Ilfov Street, No. 3, 050045, Bucharest, Romania

    M. Marin

  3. Faculty of Mechanical and Systems Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    A. Öchsner

Authors
  1. D. M. Neagu
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  2. I. M. Fudulu
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  3. M. Marin
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  4. A. Öchsner
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Correspondence to I. M. Fudulu.

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D.M.N, I.M.F, M.M, and A.O. wrote the manuscript. D.M.N and I.M.F created the images. All authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

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Neagu, D.M., Fudulu, I.M., Marin, M. et al. Wave propagation with two delay times in an isotropic porous micropolar thermoelastic material. Continuum Mech. Thermodyn. 36, 639–655 (2024). https://doi.org/10.1007/s00161-024-01287-3

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  • DOI: https://doi.org/10.1007/s00161-024-01287-3

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