Structural Engineering and Mechanics

  • 제82권4호
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  • Pages.459-467
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  • 2022
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Influence of variable thermal conductivity on waves propagating through thermo-elastic medium

  • Abo-Dahab, Sayed M. (Department of Mathematics, Faculty of Science, South Valley University) ;
  • Jahangir, Adnan (Department of Mathematics, COMSATS University Islamabad, Wah Campus) ;
  • Dar, Adiya (Department of Mathematics, COMSATS University Islamabad, Wah Campus)
  • 투고 : 2019.12.03
  • 심사 : 2022.02.11
  • 발행 : 2022.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

We investigated the influence of variable thermal conductivity on waves propagating through the elastic medium. Infinitesimal deformation results in generation of thermal signal, and is analyzed by using dual phase lag heat (DPL) conduction model. The medium considered is homogenous, isotropic and bounded by thermal shock. The elastic waves propagating through the medium are considered to be harmonic in nature, and expressions for the physical variables are obtained accordingly. Analytically, we obtained the expressions for displacement components, temperature, micro-temperature component and stresses. The theoretical results obtained are computed graphically for the particular medium by using MATLAB.

키워드

참고문헌

  1. Abd-Alla, A.M. and Yahya, G.A. (2012), "Thermal stresses in an infinite circular cylinder subjected to rotation", Appl. Math. Mech., 33(8), 1059-1078. https://doi.org/10.1007/s10483-012-1605-7.
  2. Abd-Alla, A.M., Abo-Dahab, S.M. and Kilany, A.A. (2020), "Effect of several fields on a generalized thermoelastic medium with voids in the context of Lord-Shulman or dual-phase-lag models", Mech. Bas. Des. Struct. Mach., 1-24. https://doi.org/10.1080/15397734.2020.1823852.
  3. Abo-Dahab, S.M. (2015), "Magnetic field effect on three plane waves propagation at interface between solid-liquid media placed under initial stress in the context of GL Model", Appl. Math. Inform. Sci., 9(6), 3119-3131. http://doi.org/10.12785/amis/090641.
  4. Abo-Dahab, S.M. (2016), "Electromagnetic field and rotational effects on S-waves propagation in a non-homogeneous anisotropic incompressible medium under initial stress and gravity field", Appl. Math. Inform. Sci., 10(1), 363-376. http://doi.org/10.18576/amis/100139.
  5. Abo-Dahab, S.M. and Abbas, I.A. (2011), "LS model on thermal shock problem of generalized magneto-thermoelasticity for an infinite long annular cylinder with variable thermal conductivity", Appl. Math. Model., 35(8), 3759-3769. https://doi.org/10.1016/j.apm.2011.02.028.
  6. Abo-Dahab, S.M., Abd-Alla, A.M. and Kilany, A.A. (2020), "Electromagnetic field in fiber reinforced micropolar thermoelastic medium using four models", J. Ocean Eng. Sci., 5, 230-248. https://doi.org/10.1016/j.joes.2019.12.003.
  7. Abo-Dahab, S.M., Hussein, N.S. and Alshehri, H.A. (2016), "On the rotation and axial magnetic field effects of a non-Homogeneous composite infinite cylinder of orthotropic material", Appl. Math. Inform. Sci., 10(2), 581-605. https://doi.org/10.18576/amis/100219.
  8. Abo-Dahab, S.M., Kilany, A.A., Allam, M.N M., Mohamed, R.A. and Rida S.Z. (2020), "Influence of several fields on Rayleigh waves propagation in a fiber-reinforced orthotropic half-space material under four thermoelastic models", Wave. Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2020.1849865.
  9. Abouelregal, A.E. and Abo-Dahab, S.M. (2015), "Study of the dual phase lag model of thermoelasticity fora half-space problem with rigidly fixed surface in the presence of a thermal shock", J. Comput. Theor. Nanosci., 12(1), 38-45. https://doi.org/10.1166/jctn.2015.3695.
  10. Aouadi, M. (2006), "Generalized thermo-piezoelectric problems with temperatue dependent properties", Int. J. Solid. Struct., 43(21), 6347-6358. https://doi.org/10.1016/j.ijsolstr.2005.09.003.
  11. Bayones, F.S., Abo-Dahab, S.M., Abd-Alla, A.M., Elhag S.H., Kilany, A.A. and Elsagheer M. (2021), "Initial stress and gravity on P-wave reflection from electromagneto-thermomicrostretch medium in the context of three-phase lag model", Complexity, 2021, Article ID 5560900. https://doi.org/10.1155/2021/5560900.
  12. Bayones, F.S., Kilany, A.A., Abo-Dahab, S.M. and Abd-Alla, A.M. (2022), "Electromagnentic filed and rotation for fractional derivative order calculus with temperature-dependent on reflection of longitudinal wave under initial stress and three-phase-lag model", Wave. Random Complex Media, 1-21. https://doi.org/10.1080/17455030.2022.2036385.
  13. Bayones, F.S., Kilany, A.A., Abouelregal, A.E. and Abo-Dahab, S.M. (2020), "A rotational gravitational stressed and voids effect on an electromagnetic photothermal semiconductor medium under three models of thermoelasticity", Mech. Bas. Des. Struct. Mach., 1-27. https://doi.org/10.1080/15397734.2020.1863229.
  14. Bouslimi, J., Omri, M., Kilany, A.A., Abo-Dahab, S.M. and Hatem, A. (2021), "Mathematical model on a photothermal and voids in a semiconductor medium in the context of Lord-Shulman theory", Wave. Random Complex Media, 1-18. https://doi.org/10.1080/17455030.2021.2010835.
  15. Das, J.K. and Nahid, M.A.I. (2015), "Electrical properties of thermal evaporated Bismuth Telluride thin films", Int. J. Thin Film Sci. Technol., 4, 13-16. https://doi.org/10.12785/ijtfst/040103.
  16. Ezzat, M.A., El-Karamany, A.S. and Samaan, A.A. (2004), "The dependence of the modulus of elasticity on reference temperature in generalized thermoelasticity with thermal relaxation", Appl. Math. Comput., 147(1), 169-189. https://doi.org/10.1016/S0096-3003(02)00660-4.
  17. Hashmat, A., Jahangir, A. and Aftab, K. (2020), "Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium", J. Central South Uni., 27, 3188-3201. https://doi.org/10.1007/s11771-020-4472-1.
  18. Iesan, D. and Quintanilla R. (2000), "On a theory of thermoelasticity with micro-temperatures", J. Therm. Stress., 23(3), 199-215. https://doi.org/10.1080/014957300280407.
  19. Khalil, E.M., Abo-Dahab, S.M. and Kilany, A.A. (2021), "Electromagnetic field and initial stress on a photothermal semiconducting voids medium under thermoelasticity theories", Math. Meth. Appl. Sci., 44, 7778-7798. https://doi.org/10.1002/mma.6942.
  20. Liu, Z., Ramon, Q. and Yang, W. (2021), "Dual phase lag heat conduciton with microtemperatures", ZAMM-J. Appl. Math. Mech./Zeitschrift fur Angewandte Mathematik und Mechanik, 101(12), e202000167. https://doi.org/10.1002/zamm.202000167.
  21. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Cont. Mech. Thermodyn., 28, 1645-1657. https://doi.org/10.1007/s00161-016-0503-4.
  22. Marin, M., Rehman, E. and Adina C. (2017), "On the solution of Saint-Venant's problem for elastic dipolar bodies with voids", Carpath. J., 33(2), 2019-232.
  23. Marin, M., Vlase, S., Ellahi, R. and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry, 11(7), 863-873. https://doi.org/10.3390/sym11070863.
  24. Mondal, S., Mallik, S.H. and Kanoria, M. (2014), "Fractional order two-temperature dual-phase-lag thermo-elasticity with variable thermal conductivity", Int. Schol. Res. Notic., 7(2), 1-13. https://doi.org/10.1155/2014/646049.
  25. Parveen, L. and Kaur, I. (2019), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., 37(2), 245-253. https://doi.org/10.12989/sem.2019.70.2.245.
  26. Prasad, R., Kumar, R. and Mukhopadhyay, S. (2010), "Propagation of harmonic plane waves under thermo-elasticity with dual phase lags", Int. J. Eng. Sci., 48(12), 2028-2043. https://doi.org/10.1016/j.ijengsci.2010.04.011.
  27. Quintanilla, R. and Rache, R. (2006), "A note on stability in dual phase lag heat conduction", Int. J. Heat Mass Transf., 49(7), 1209-1213. https://doi.org/10.1016/j.ijheatmasstransfer.2005.10.016.
  28. Singh, B. (2013), "Wave propagation in dual-phase-lag anisotropic thermo-elasticity", Continuum Mech. Thermodyn., 25(5), 675-683. https://doi.org/10.1007/s00161-012-0261-x.
  29. Steeb, H., Singh, J. and Tomar, S.K. (2013), "Time harmonic waves in thermoelastic materials with micro temperatures", Mech. Res. Commun., 48(1), 8-13. https://doi.org/10.1016/j.mechrescom.2012.11.006.
  30. Tzou, D.Y. (1995), "A unified filed approach for heat conduction from macro to micro scales", J. Heat Transf., 117(1), 8-16. https://doi.org/10.1115/1.2822329.
  31. Wang, Y., Liu, D., Wang, Q. and Zhou, J. (2016), "Asymptotic solutions for generalized thermoelasticity with variable thermal material properties", Arch. Mech., 68(3), 181-202.
  32. Youssef, H.M. (2005), "Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity", Appl. Math. Mech., 26(4), 470-475. https://doi.org/10.1007/BF02465386.
  33. Youssef, H.M. (2005), "State-Space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to Ramp-type heating", Can. Appl. Math. Quart., 13(4), 369-390.
  34. Youssef, H.M. and Abbas, I.A. (2007), "Thermal shock problem of generalized thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity", Comput. Meth. Sci. Technol., 13(2), 95-100. https://doi.org/10.12921/cmst.2007.13.02.95-100.
  35. Zenkou, A.M. (2006), "Thermoelastic solutions for annular disks with arbitrary variable thickness", Struct. Eng. Mech., 24(5), 515-528. https://doi.org/10.12989/sem.2006.24.5.515.