Coupled systems mechanics

  • 제9권4호
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  • Pages.325-342
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  • 2020
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Memory response in elasto-thermoelectric spherical cavity

  • El-Attar, Sayed I. (Department of Mathematics, Faculty of Science, Northern Border University) ;
  • Hendy, Mohamed H. (Department of Mathematics, Faculty of Science, Northern Border University) ;
  • Ezzat, Magdy A. (Department of Mathematics, College of Science and Arts, Al-Qassim University)
  • 투고 : 2019.09.09
  • 심사 : 2020.01.08
  • 발행 : 2020.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

A mathematical model of electro-thermoelasticity subjected to memory-dependent derivative (MDD) heat conduction law is applied to a one-dimensional problem of a thermoelectric spherical cavity exposed to a warm stun that is an element of time in the presence of a uniform magnetic field. Utilizing Laplace transform as an instrument, the issue has been fathomed logically within the changed space. Numerical inversion of the Laplace transform is carried for the considered distributions and represented graphically. Some comparisons are shown in the figures to estimate the effects of MDD parameters and thermoelectric properties on the behavior of all considered fields.

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참고문헌

  1. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103.
  2. Alzahrani, F.S. and Abbas, I.A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., 22(2), 369-386. https://doi.org/10.12989/scs.2016.22.2.369.
  3. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351.
  4. Bo, Y., Xiaoyun, J. and Huanying, X. (2015), "A novel compact numerical method for solving the two dimensional non-linear fractional reaction-subdiffusion equation", Numer. Algor., 68(4), 923-950. https://doi.org/10.1007/s11075-014-9877-1.
  5. Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity. a review of recent literature", Appl. Mech. Rev., 51(12), 705-729. https://doi.org/10.1007/s11075-014-9877-1.
  6. Ezzat, M.A. (2004), "Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region", Int. J. Eng. Sci., 42, 1503-1519. https://doi.org/10.1016/j.ijengsci.2003.09.013.
  7. Ezzat, M.A. (2006), "The relaxation effects of the volume properties of electrically conducting viscoelastic material", Mater. Sci. Eng. B: Solid-State Mater. Adv. Technol., 130(1-3), 11-23. https://doi.org/10.1016/j.mseb.2006.01.020.
  8. Ezzat, M.A. and El-Bary, A.A. (2017a), "Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. https://doi.org/10.12989/scs.2017.24.3.297.
  9. Ezzat, M.A. and El-Bary, A.A. (2017b), "A functionally graded magneto-thermoelastic half space with memory-dependent derivatives heat transfer", Steel. Compos. Struct., 25(2), 177-186. https://doi.org/10.12989/scs.2017.25.2.177.
  10. Ezzat, M.A. and Youssef, H.M. (2010), "Stokes' first problem for an electro-conducting micropolar fluid with thermoelectric properties", Can. J. Phys., 88, 35-48. https://doi.org/10.1139/P09-100.
  11. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2014), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23, 545-553. https://doi.org/10.1080/15376494.2015.1007189.
  12. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2016), "Electro-thermoelasticity theory with memory-dependent derivative heat transfer", Int. J. Eng. Sci., 99, 22-38. https://doi.org/10.1016/j.ijengsci.2015.10.011.
  13. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017), "Thermoelectric viscoelastic materials with memory-dependent derivative", Smart. Struc. Syst., 19, 539-551. http://dx.doi.org/10.12989/sss.2017.19.5.539.
  14. Ezzat, M.A., Othman, M.I. and El-Karamany, A.S. (2001), "State space approach to generalized thermo-viscoelasticity with two relaxation times", Int. J. Eng. Sci., 40(3), 283-302. https://doi.org/10.1016/S0020-7225(01)00045-3.
  15. Ezzat, M.A., Zakaria, M., Shaker, O. and Barakat, F. (1996), "State space formulation to viscoelastic fluid flow of magnetohydrodynamic free convection through a porous medium", Acta Mech., 119, 147-164. https://doi.org/10.1007/BF01274245.
  16. Fox, N. (1969), "Generalized thermoelasticity", Int. J. Eng. Sci., 7, 437-445. https://doi.org/10.1080/014957399280832.
  17. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elasticity, 2, 1-7. https://doi.org/10.1007/BF00045689.
  18. He, T., Zhang, P., Xu, C. and Li, Y. (2019), "Transient response analysis of a spherical shell embedded in an infinite thermoelastic medium based on a memory-dependent generalized thermoelasticity", J. Therm. Stress., 48 (8), 943-961. https://doi.org/10.1080/01495739.2019.1610342.
  19. Hetnarski, R.B. and Ignaczak, J. (2000), "Nonclassical dynamical thermoelasticity", Int. J. Solid. Struct., 37, 215-224. https://doi.org/10.1016/S0020-7683(99)00089-X.
  20. Hiroshige, Y., Makoto, O. and Toshima, N. (2007), "Thermoelectric figure-of-merit of iodine-doped copolymer of phenylenevinylene with dialkoxyphenylenevinylene", Synthetic Metal., 157, 467-474. https://doi.org/10.1016/j.synthmet.2007.05.003.
  21. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of the Laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  22. Ignaczak, J. and Ostoja-starzeweski, M. (2009), Thermoelasticity with Finite Wave Speeds, Oxford University Press, Oxford, UK.
  23. Kothari, S. and Mukhopadhyay, S. (2011), "A problem on elastic half space under fractional order theory of thermoelasticity", J. Therm. Stress., 34, 724-739. https://doi.org/10.1080/01495739.2010.550834.
  24. Lata, P. (2018a), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113.
  25. Lata, P. (2018b), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Comps. Struct., 27(4), 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
  26. Lata, P. (2019), "Time harmonic interactions in fractional thermoelastic diffusive thick circular plate", Coupl. Syst. Mech., 8(1), 39-53. https://doi.org/10.12989/csm.2019.8.1.039.
  27. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22, 567-587. http://dx.doi.org/10.12989/scs.2016.22.3.567.
  28. Li, Y., Zhang, P., Li, C. and He, Y. (2019), "Fractional order and memory-dependent analysis to the dynamic response of a bi-layered structure due to laser pulse heating", Int. J. Heat Mass Trans., 44(12), 118664. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118664.
  29. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  30. Marin, M. and Craciun, E.M. (2017), "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials", Comps. B: Eng., 126(1), 27-37. https://doi.org/10.1016/j.compositesb.2017.05.063.
  31. Marin, M. and Florea, O. (2014), "On temporal behavior of solutions in thermoelasticity of porous micropolar bodies", An. St. Univ. Ovidius Constanta, 22, 169-188. https://doi.org/10.2478/auom-2014-0014.
  32. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continu. Mech. Thermodyn., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4.
  33. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by Lagrange's identity", Bound. Value Prob., 2013, 135. https://doi.org/10.1186/1687-2770-2013-135.
  34. Marin, M., Baleanu, D. and Valse, S. (2017), "Effect of microtemperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61(3), 381-387. https://doi.org/10.12989/sem.2017.61.3.381.
  35. Morelli, D.T. (1997), Thermoelectric Devices, Eds. G.L. Trigg, and E.H. Immergut, Encyclopedia of Applied Physics, Wiley-VCH, New York.
  36. Mukhopadhyay, S. and Kumar, R. (2009), "Thermoelastic interactions on two-temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity", J. Therm. Stress., 32, 341-360. https://doi.org/10.1080/01495730802637183.
  37. Othman, M.I., Ezzat, M.A., Zaki, S.A. and El-Karamany, A.S. (2002), "Generalized thermo-viscoelastic plane waves with two relaxation times", Int. J. Eng. Sci., 40, 1329-1347. https://doi.org/10.1016/S0020-7225(02)00023-X.
  38. Povstenko, Y.Z. (2004), "Fractional heat conductive and associated thermal stress", J. Therm. Stress., 28, 83-102. https://doi.org/10.1080/014957390523741.
  39. Rowe, D.M. (1995), Handbook of Thermoelectrics, CRC Press.
  40. Shaw, S. (2019), "Theory of generalized thermoelasticity with memory-dependent derivatives", J. Eng. Mech., 145, 04019003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001569.
  41. Shercliff, J.A. (1979), "Thermoelectric magnetohydrodynamics", J. Fluid Mech., 191, 231-251. https://doi.org/10.1017/S0022112079000136.
  42. Shereif, H.H. (1992), "Fundamental solution for thermoelasticity with two relaxation times", Int. J. Eng. Sci., 30(7), 861-870. https://doi.org/10.1016/0020-7225(92)90015-9.
  43. Sherief, H.H. and El-Latief, A.M. (2016), "Modeling of variable Lame's Modulii for a FGM generalized thermoelastic half space", Lat. Am. J. Solid. Struct., 13, 715-730. https://doi.org/10.1590/1679-78252086.
  44. Sherief, H.H., El-Said, A.A. and Abd El-Latief, A. (2010), "Fractional order theory of thermo-elasticity", Int. J. Solid. Struct., 47, 269-275. https://doi.org/10.1016/j.ijsolstr.2009.09.034.
  45. Tiwari, R. and Mukhopadhyay, S. (2018), "Analysis of wave propagation in the presence of a continuous line heat source under heat transfer with memory dependent derivatives", Math. Mech. Solid., 23, 820-834. https://doi.org/10.1177/1081286517692020.
  46. Tritt, T.M. (1999), "Thermoelectric materials new directions and approaches", Mat. Res. Soc. Symp. Proc., 545, 233-246.
  47. Tritt, T.M. (2000), Semiconductors and Semimetals, Recent Trends in Thermoelectric Materials Research, Academic Press, San Diego.
  48. Wang, J.L. and Li, H.F. (2011), "Surpassing the fractional derivative: Concept of the memory-dependent derivative", Comput. Math. Appl., 62, 1562-1567. https://doi.org/10.1016/j.camwa.2011.04.028.
  49. Xue, Z.N., Chen, Z.T. and Tian, X.G. (2018), "Thermoelastic analysis of a cracked strip under thermal impact based on memory-dependent heat conduction model", Eng. Fract. Mech., 200, 479-498. https://doi.org/10.1016/j.engfracmech.2018.08.018.
  50. Youssef, H. (2010), "Theory of fractional order generalized thermoelasticity", J. Heat. Transf., 132(6), 061301-7. https://doi.org/10.1115/1.4000705.
  51. Yu, Y.J., Tian, X.G. and Lu, T.J. (2013), "Fractional order generalized electro-magnetothermo-elasticity", Eur. J. Mech., A/Solid., 42, 188-202. https://doi.org/10.1016/j.euromechsol.2013.05.006.
  52. Zenkour, A.M. (2017), "Vibration analysis of generalized thermoelastic microbeams resting on visco-Pasternak", Adv. Aircraft Spacecraft Sci., 4(3), 267-280. http://dx.doi.org/10.12989/aas.2017.4.3.267.
  53. Zhang, H., Xiaoyun, J. and Xiu, Y. (2018), "A time-space spectral method for the time-space fractional Fokker-Planck equation and its inverse problem", Appl. Math. Comput., 320, 302-318. https://doi.org/10.1016/j.amc.2017.09.040.