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Frequency-domain analysis of transversely isotropic thermoelastic diffusive solid with two-temperature

  • Parveen Lata (Department of Mathematics, Punjabi University) ;
  • Heena (Department of Mathematics, Punjabi University)
  • 투고 : 2025.04.09
  • 심사 : 2025.10.15
  • 발행 : 2025.10.25

초록

This study investigates the deformations in a two-dimensional transversely isotropic thermoelastic medium with diffusion under the effect of two-temperature in frequency domain. The analysis is carried out using the Green and Naghdi theory of thermoelasticity with and without energy dissipation. Fourier transformation technique is used to solve the problem and then numerical inversion technique is applied to obtain the results in physical domain. Concentrated and uniformly distributed loads are considered to illustrate the model. Graphical representation of variation in the field variables with distance is depicted by taking the effect of two-temperature and frequency.

키워드

참고문헌

  1. Abbas, I.A. (2009), "Effect of thermal dispersion on free convection in a fluid saturated porous medium", Int. J. Heat Fluid Flow, 30(2), 229-236. https://doi.org/10.1016/j.ijheatfluidflow.2009.01.004.
  2. Abbas, I.A., Kumar, R. and Chawla, V. (2012), "Response of thermal source in a transversely isotropic thermoelastic half-space with mass diffusion by using a finite element method", Chinese Phys. B, 21, 084601. http://doi.org/10.1088/1674-1056/21/8/084601.
  3. Abbas, I.A. and Othman, M.I.A. (2012), "Plane waves in generalized thermo-microstretch elastic solid with thermal relaxation using finite element method", Int. J. Thermophys., 33, 2407-2423. http://doi.org/10.1007/s10765-012-1340-8.
  4. Kumar, R., Gupta, V. and Abbas, I.A. (2013), "Plane deformation due to thermal source in fractional order thermoelastic media", J. Comput. Theor. Nanosci., 10, 2520-2525. http://doi.org/10.1166/jctn.2013.3241
  5. Abbas, I.A. (2014), "A GN model based upon two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity", Appl. Math. Comput., 245, 108-115. http://doi.org/10.1016/j.amc.2014.07.059.
  6. Abbas, I.A. (2014), "A problem on functional graded material under fractional order theory of thermoelasticity", Theor. Appl. Fract. Mech., 74, 18-22. http://doi.org/10.1016/j.tafmec.2014.05.005
  7. Abbas, I.A. (2015), "A GN model for thermoelastic interaction in a microscale beam subjected to a moving heat source", Acta Mechanica, 226, 2527-2536. http://doi.org/10.1007/s00707-015-1340-4.
  8. Abbas, I.A. and Youssef, H.M. (2015), "Two-dimensional fractional order generalised thermoelastic porous material", Latin Am. J. Solids Struct., 12, 1415-1431. http://doi.org/10.1590/1679-78251584.
  9. Alzahrani, F.S. and Abbas, I.A. (2020), "Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model", Mathematics, 8(4), 585. https://doi.org/10.3390/math804 0585.
  10. Abbas, I.A., Saeed, T. and Alhothuali, M. (2020), "Hyperbolic two-temperature photo-thermal interaction in a semiconductor medium with a cylindrical cavity", Silicon, 13, 1871-1878. https://doi.org/10.1007/s12633-020-00570-7.
  11. Abbas, I.A. (2024), "Analytic solutions of photo-thermal interaction in a semiconductor medium upon the new hyperbolic two-temperature theory", Waves Random Complex Med., 34(3), 1095-1109. https://doi.org/10.1080/17455030.2021.1928329.
  12. Abouelregal, A.E., Askar, S.S., Marin, M. and Mohamed, B. (2023), "The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod", Sci. Rep., 13(1), 9052. https://doi.org/10.1038/s41598-023-36371-2.
  13. Alzahrani, F.S. and Abbas, I.A. (2020), "Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model", Mathematics, 8(4), 585. https://doi.org/10.3390/math804 0585.
  14. Aouadi, M., Passarella, F. and Tibullo, V. (2023), "Stability of thermoelastic diffusion problem of type III in spaces of different dimensions", ZAMM J. Appl. Math. Mech., 103(10), e202200591. https://doi.org/10.1002/zamm.202200591.
  15. Atwa, S.Y., Ammar, M.K. and Ibrahim, E. (2017), "The effect of two-temperature on thermoelastic medium with diffusion due to three phase-lag model", Appl. Math. Nonlinear Sci., 2(1), 259-270. https://doi.org/10.21042/AMNS.2017.1.00022
  16. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351.
  17. Chawla, V. and Kamboj, D. (2020), "A general study of fundamental solutions in aniotropicthermoelastic media with mass diffusion and voids", Int. J. Appl. Mech. Eng., 25(4), 22-41. http://doi.org/10.2478/ijame-2020-0047.
  18. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys., 19(4), 969-970. https://doi.org/10.1007/BF01594969.
  19. Chen, P.J. and Williams, W.O. (1968), "A note on non-simple heat conduction", J. Appl. Math. Phys., 19(6), 614-627. https://doi.org/10.1007/BF01602278.
  20. Chen, P.J., Gurtin M.E. and Williams W.O. (1969), "On the thermodynamics of non-simple elastic materials with two-temperatures", J. Appl. Math. Phys., 20(1), 107-112. https://doi.org/10.1007/BF01591120.
  21. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan publ. Corp., New Delhi, India.
  22. El-Sapa, S., El-Bary, A.A. and Atef, H.M. (2023), "Modeling the viscosity and rotation on a generalized micropoloar thermoelasticity with two-temperature under five theories", Waves Random Complex Med., 15, 1-25. https://doi.org/10.1080/17455030.2023.2184646.
  23. Green, A.E. and Lindsay, K. (1972), "Thermoelasticity", J. Elastic., 2(1), 1-7. https://doi.org/10.1007/BF00045689.
  24. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15, 253-264. http://doi.org/10.1080/01495739208946136.
  25. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elastic., 31, 189-208. https://doi.org/10.1007/BF00044969.
  26. Hobiny, A., Abbas, I. and Marin, M. (2022), "The influences of hyperbolic two-temperatures theory on waves propagation in a semiconductor material containing spherical cavity", Mathematics, 10(1), 121. https://doi.org/10.3390/math10010121.
  27. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.
  28. Kaur, I., Lata, P. and Singh, K. (2021), "Study of frequency shift and thermoelastic damping in transversely isotropic nanobeam with GN III theory and two temperature", Arch. Appl. Mech., 91(4), 1-15. https://doi.org/10.1007/s00419-020-01848-3.
  29. Lata, P. and Heena (2024), "Thermomechanical interactions in a transversely isotropic thermoelastic media with diffusion due to inclined load", Struct. Eng. Mech., 90(3), 263-272. https://doi.org/10.12989/sem.2024.90.3.263.
  30. Lata, P. and Singh, S. (2022), "Effect of rotation and inclined load in a nonlocal magneto-thermoelastic solid with two-temperature", Adv. Mater. Res., 11(1), 23-39. https://doi.org/10.12989/amr.2022.11.1.023.
  31. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  32. Marin, M. (2010), "A partition of energy in thermoelasticity of microstretch bodies", Nonlinear Anal. Real World Appl., 11(4), 2436-2447. https://doi.org/10.1016/j.nonrwa.2009.07.014.
  33. Marin, M. and Florea, O. (2014). "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", Analele Universitatii Ovidius Constanta - Seria Matematica, 22(1), 169-188. http://doi.org/10.2478/auom-2014-0014.
  34. Nowacki, W. (1974), "Dynamic problems of thermodiffusion in elastic solids", Proceedings of Vibrational Problems, 15, 105-128.
  35. Nowacki, W. (1975), "Thermodiffusion in solids", J. Theor. Appl. Mech., 13(2), 143-158.
  36. Nowacki, W. (1976), "Dynamic problems of diffusion in solids", Eng. Fract. Mech., 8(1), 261-266. https://doi.org/10.1016/0013-7944(76)90091-6.
  37. Othman, M.I.A., Atwa, S.Y. and Farouk, R.M. (2009), "The effect of dkiffusion on two-dimensional problem of generalized thermoelasticity with Green-Naghdi theory", Int. Commun. Heat Mass Transf., 36(8), 857- 864. https://doi.org/10.1016/j.icheatmasstransfer.2009.04.014
  38. Press, W.H., Teukolsky, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes In Fortran, Cambridge university press, Cambridge, U.K.
  39. Sharma, N., Kumar, R. and Ram, P. (2010), "Elastodynamic response of thermoelastic diffusion due to inclined load", Multidiscipl. Model. Mater., 6(3), 313-334. https://doi.org/10.1108/1573610101108008.
  40. Sharma, K.D., Kumar, R., Kakkar, M. and Ghangas, S. (2021), "Three dimensional waves propagation in thermos-viscoelastic medium with two temperature and void", IOP Conference Series: Mater. Sci. Eng., 1033(1), 012059. https://doi.org/10.1088/1757-899X/1033/1/012059.
  41. Sharma, S., Devi, S., Kumar, R. and Marin, M. (2024), "Examining basic theorems and plane waves in the context of thermoelastic diffusion using a multi-phase-lag model with temperature dependence", Mech. Adv. Mater. Struct., 1-18. https://doi.org/10.1080/15376494.2024.2370523.
  42. Sharma, S., Marine, M. and Altenbach, H. (2025), "Elastodynamic interactions in thermoelastic diffusion including non-local and phase-lags", ZAMM-J. Appl. Math. Mech., 105(1), e202401059. https://doi.org/10.1002/zamm.202401059.
  43. Sherief, H.H., Hamza, F.A. and Saleh, H.A. (2004), "The theory of generalized thermoelastic diffusion", Int. J. Eng. Sci., 42(5-6), 591-608. https://doi.org/10.1016/j.ijengsci.2003.05.001.
  44. Sherief, H.H. and Saleh, H.A. (2005), "A half-space problem in the theory of generalized thermoelastic diffusion", Int. J. Solids Struct., 42(15), 4484-4493. https://doi.org/10.1016/j.ijsolstr.2005.01.001.
  45. Sur, A. and Kanoria, M. (2016), "Three dimensional viscoelastic medium under thermal shock", Eng. Solid Mech., 4(4), 187-200. https://doi.org/10.5267/j.esm.2016.6.002
  46. Youssef, H.M. (2006), "Theory of two-temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. https://doi.org/10.1093/imamat/hxh101.
  47. Zeeshan, A., Khan, M.I., Ellahi, R. and Marin, M. (2023), "Computational intelligence approach for optimising MHD casson ternary hybrid nanofluid over the shrinking sheet with the effects of radiation", Appl. Sci., 13(17), 9510. https://doi.org/10.3390/app13179510.
  48. Zenkour, A.M. (2022), "Thermal diffusion of an unbounded solid with a spherical cavity via refined three-phase-lag Green-Naghdi models", Indian J. Phys., 96(4), 1087-1104. https://doi.org/10.1007/s12648-021-02042-z.