DOI QR코드

DOI QR Code

Effect of the gravity on a nonlocal micropolar thermoelastic media with the multi-phase-lag model

  • Samia M. Said (Department of Mathematics, Faculty of Science, Zagazig University)
  • Received : 2022.09.01
  • Accepted : 2023.11.28
  • Published : 2024.01.10

Abstract

Erigen's nonlocal thermoelasticity model is used to study the effect of viscosity on a micropolar thermoelastic solid in the context of the multi-phase-lag model. The harmonic wave analysis technique is employed to convert partial differential equations to ordinary differential equations to get the solution to the problem. The physical fields have been presented graphically for the nonlocal micropolar thermoelastic solid. Comparisons are made with the results of three theories different in the presence and absence of viscosity as well as the gravity field. Comparisons are made with the results of three theories different for different values of the nonlocal parameter. Numerical computations are carried out with the help of Matlab software.

Keywords

References

  1. Abd-Alla, A.N. and Abo-Dahab, S.M. (2009), "Time-harmonic sources in a generalized magneto-thermoviscoelastic continuum with and without energy dissipation", Appl. Math. Model., 33(5), 2388-2402. https://doi.org/10.1016/j.apm.2008.07.008. 
  2. Aljadani, M.H. and Zenkour, A.M. (2022a), "A modified tworelaxation thermoelastic model for a thermal shock of rotating infinite medium", Materials, 15(24), 9056. https://doi.org/10.3390/ma15249056. 
  3. Aljadani, M.H. and Zenkour, A.M. (2022b), "Effect of hydrostatic initial stress on a rotating half-Space in the context of a tworelaxation power-law model", Mathematics, 10(24), 4727. https://doi.org/10.3390/math10244727. 
  4. Alfrey, T.T. and Gurnee, E.F. (1956), "Dynamics of viscoelastic behavior, in: Rheology", Theory Appl., 387-429. https://doi.org/10.1016/B978-0-12-395694-1.50017-8. 
  5. Baljeet, S. (2021), "Nonlocal effects on propagation of waves in a generalized thermoelastic solid half space", Struct. Eng. Mech., 77(4), 473-479. https://doi.org/10.12989/sem.2021.77.4.473. 
  6. Balta, F. and Suhubi, E.S. (1977), "Theory of nonlocal generalized thermoelasticity", Int. J. Eng. Sci., 15(9-10), 577-588. https://doi.org/10.1016/0020-7225(77)90054-4. 
  7. Bayones, F.S. (2012), "The influence of diffusion on generalized magneto-thermo-viscoelastic problem of a homogenyous isotropic material", Adv. Theor. Appl. Mech., 5(2), 69-92. http://www.m-hikari.com/atam/atam2012/atam1-4-2012/bayonesATAM1-4-2012.pdf. 
  8. Choudhuri, S.R. (2007), "On a thermoplastic three-phase-lag model", J. Therm. Stresses, 30(3), 231-238. https://doi.org/10.1080/01495730601130919. 
  9. Eringen, A.C. (1974), "Theory of nonlocal thermoelasticity", Int. J. Eng. Sci., 12(12), 1063-1077. https://doi.org/10.1016/0020- 7225(74)90033-0. 
  10. Eringen, A.C. (1973), "Linear theory of micropolar elasticity", J. Appl. Math. Mech., 15(6), 909-924. https://www.jstor.org/stable/24901442. 
  11. Ferry, J.D. (1980), "Viscoelastic properties of polymers", 3rd Ed., John Wiley & Sons. https://www.wiley.com/enus/9780471048947. 
  12. Hetnarski, R.B. and Ignaczak, J. (1999), "Generalized thermoelasticity", J. Therm. Stresses, 22(4-5), 451-476. https://doi.org/10.1080/014957399280832. 
  13. Hetnarski, R.B. and Ignaczak, J. (2000), "Nonclassical dynamical thermoelasticity", Int. J. Solids Struct., 37(1-2), 215-224. https://doi.org/10.1016/S0020-7683(99)00089-X. 
  14. Hobiny, A., Abbas, A., Alshehri, I. and Marin, M. (2022), "Analytical solutions of nonlocal thermoelastic Interaction on semi-infinite mediums induced by ramp-type heating", Symmetry, 14(5), 864. https://doi.org/10.3390/sym14050864. 
  15. Inan, E. and Eringen, A.C. (1991), "Nonlocal theory of wave propagation in thermoelastic plates", Int. J. Eng. Sci., 29(7), 831-843. https://doi.org/10.1016/0020-7225(91)90005-N. 
  16. Kalkal, K.K., Sheoran, D. and Deswal, S. (2020), "Reflection of plane waves in a nonlocal micropolar thermoelastic medium under the effect of rotation", Acta Mech., 231(7), 2849-2866. https://doi.org/10.1007/s00707-020-02676-w. 
  17. Koutsoumaris, C., Eptaimeros, K.G. and Tsamasphyros, G.J. (2017), "A different approach to Eringen.s nonlocal integral stress model with applications for beams", Int. J. Sol. Struct. 112, 222-238. https://doi.org/10.1016/j.ijsolstr.2016.09.007. 
  18. Kumar, R., Chawla, V. and Abbas, I.A. (2012), "Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model", Theor. Appl. Mech., 39(4), 313-341. http://www.doiserbia.nb.rs/img/doi/1450-5584/2012/1450-55841204313K.pdf.  https://doi.org/10.2298/TAM1204313K
  19. Liew, K.M., Zhang, Y. and Zhang, L.W. (2017), "Nonlocal elasticity theory for grapheme modeling and simulation: Prospects and challenges", J. Model. Mech. Mat., 20160159. https://doi.org/10.1515/jmmm-2016-0159. 
  20. Marin, M., Ellahi, R., Vlase, S. and Bhatti, M.M. (2020a), "On the decay of exponential type for the solutions in a dipolar elastic body", J. Taibah Univ. Sci., 14(1), 534-540. https://doi.org/10.1080/16583655.2020.1751963. 
  21. Montanaro, A. (1999), "On singular surfaces in isotropic linear thermoelasticity with initial stress", J. Acoust Soc. Am., 106(3), 1586-1588. https://doi.org/10.1121/1.427154. 
  22. Mukhopadhyay, S. (2000), "Effects of thermal relaxations on thermo-visco-elastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary", J. Therm. Stress, 23(7), 675-684. https://doi.org/10.1080/01495730050130057. 
  23. Othman, M.I.A. (2004), "Generalized electromagnetothermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time", Acta Mech., 169(5), 37-51. https://doi.org/10.1007/s00707-004-0101-6. 
  24. Othman, M.I.A., Said, S.M. and Marin, M. (2019), "A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with threephase-lag model", Int. J. Numer. Meth. Heat Fluid Fl., 29(12), 4788-4806. https://doi.org/10.1108/HFF-04-2019-0359. 
  25. Said, S.M. (2020a), "Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity", Appl. Math. Mech., 41(3), 819-832. https://doi.org/10.1007/s10483-020-2603-9. 
  26. Said, S.M. (2020b), "The effect of mechanical strip load on a magneto-micropolar thermoelastic medium: Comparison of four different theories", Mech. Res. Commun., 107, 103549. https://doi.org/10.1016/j.mechrescom.2020.103549. 
  27. Said, S.M. (2022), "A viscoelastic-micropolar solid with voids and microtemperatures under the effect of the gravity field", Geomech. Eng., 31(2), 159-166. https://doi.org/10.12989/gae.2022.31.2.159. 
  28. Said, S.M. (2023), "A novel model of a nonlocal porous thermoelastic solid with temperature-dependent properties using an eigenvalue approach", Geomech. Eng., 32(2), 137-144. https://doi.org/10.12989/gae.2023.32.2.137. 
  29. Samanta, S.C. and Maisha, R.K. (2008), "A study on magnetothermo-viscoelastic interactions in an elastic half-space subjected to a temperature pulse, using state space approach", J. Therm. Stresses, 31(12), 1149-1169. https://doi.org/10.1080/15313220802507867. 
  30. Sarkar, N. and Tomar, S.K. (2019), "Waves in dual-phase-lag thermoelastic materials with voids based on Eringen's nonlocal elasticity", J. Therm. Stresses, 42(8), 580-606. https://doi.org/10.1080/01495739.2019.1591249. 
  31. Scutaru, M.L., Vlase, S., Marin, M. and Modrea, A. (2020b), "New analytical method based on dynamic response of planar mechanical elastic systems", Bound Value Probl., 2020, 104. https://doi.org/10.1186/s13661-020-01401-9. 
  32. Tzou, D.Y. (1995),"A unified field approach for heat conduction from macro-to micro-scales", ASME J. Heat Transf. 117(1), 8-16. https://doi.org/10.1115/1.2822329. 
  33. Tschoeg, N.W. (1997), "Time dependence in material properties: An overview", Mech. Time-Dep. Mat., 1(3), 3-31. https://doi.org/10.1023/A:1009748023394. 
  34. Zenkour, A.M. (2018), "Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis", Acta Mech., 229(9), 3671-3692. https://doi.org/10.1007/s00707-018-2172-9. 
  35. Zenkour, A.M. (2020a), "Wave propagation of a gravitated piezothermoelastic half-space via a refined multi-phase-lags theory", Mech. Adv. Mater. Struct., 27(22), 1923-1934. https://doi.org/10.1080/15376494.2018.1533057. 
  36. Zenkour, A.M. (2020b), "Magneto-thermal shock for a fiberreinforced anisotropic half-space studied with a refined multidual-phase-lag model", J. Phys. Chem. Solids, 137, 109213. https://doi.org/10.1016/j.jpcs.2019.109213. 
  37. Zenkour, A.M. (2020c), "Thermal-shock problem for a hollow cylinder via a multi-dual-phase-lag theory", J. Therm. Stress., 43(6), 687-706. https://doi.org/10.1080/01495739.2020.1736966. 
  38. Zenkour, A.M. (2020d), " Exact coupled solution for photothermal semiconducting beams using a refined multi-phase-lag theory", Opt. Laser Technol., 128, 106233. https://doi.org/10.1016/j.optlastec.2020.106233. 
  39. Zenkour, A.M. and El-Mekawy, H.F. (2020), "On a multi-phaselag model of coupled thermoelasticity", Int. Commun. Heat Mass Transfer., 116, 104722. https://doi.org/10.1016/j.icheatmasstransfer.2020.104722. 
  40. Zenkour, A.M., Saeed, T. and Aati, A.M. (2023), "Refined dualphase-lag Theory for the 1D behavior of skin tissue under ramptype heating", Materials, 16(6), 2421. https://doi.org/10.3390/ma16062421. 
  41. Zenkour, A.M. and El-Shahrany, H.D. (2023), "Vibration of viscoelastic magnetostrictive plates embedded in viscoelastic foundations in hygrothermal environments", Acta Mech. Sin., 39, 522305. https://doi.org/10.1007/s10409-022-22305-x.