Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Fiber-reinforced micropolar thermoelastic rotating Solid with voids and two-temperature in the context of memory-dependent derivative

  • Alharbi, Amnah M. (Department of Mathematics, College of Science, Taif Univeristy) ;
  • Said, Samia M. (Department of Mathematics, Faculty of Science, Zagazig University) ;
  • Abd-Elaziz, Elsayed M. (Department of Basic Scineces, Zagazig Higher Institute of Eng. and Tech.) ;
  • Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University)
  • Received : 2021.09.30
  • Accepted : 2022.02.09
  • Published : 2022.02.25
⟨ Previous Next ⟩

Abstract

The main concern of this article is to discuss the problem of a two-temperature fiber-reinforced micropolar thermoelastic medium with voids under the effect rotation, mechanical force in the context four different theories with memory-dependent derivative (MDD) and variable thermal conductivity. The three-phase-lag model (3PHL), dual-phase-lag model (DPL), Green-Naghdi theory (G-N II, G-N III), coupled theory, and the Lord-Shulman theory (L-S) are employed to solve the present problem. Analytical expressions of the physical quantities are obtained by using Laplace-Fourier transforms technique. Numerical results are shown graphically and the results obtained are analyzed. The most significant points are highlighted.

Keywords

Acknowledgement

The authors thank Taif University Researchers Supporting Project Number (TURSP-2020/230), Taif University, Taif, Saudi Arabia.

References

  1. Abbas, I.A. and Marin, M. (2018), "Analytical solutions of a twodimensional generalized thermoelastic diffusions problem due to laser pulse", Iran. J. Sci. and Tech. Trans. of Mech. Eng., 42(1), 57-71. https://doi.org/10.1007/s40997-017-0077-1.
  2. Barak, M.S. and Kaliraman, V. (2014), "Reflection and transmission of elastic waves from an imperfect boundary between micropolar elastic solid half space and fluid saturated porous solid half space", Mech. Adv. Mater. Struct., 21(9), 697-709. https://doi.org/10.1080/15376494.2018.1432795.
  3. Belfield, A.J., Rogers, T.G. and Spencer, A.J.M. (1983), "Stress in elastic plates reinforced by fibre lying in concentric circles", J. Mech. Phys. Solids, 31, 25-54. https://doi.org/10.1016/0022-5096(83)90018-2
  4. Caputo, M. (1967), "Linear models of dissipation whose Q is almost frequency independent II", Geophys. J. Int., 13, 529-539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x.
  5. Caputo, M. and Mainardi, F. (1971), "Linear model of dissipation in an elastic solids", La Rivista del Nuovo Cimento, 1, 161-198. https://doi.org/10.1007/BF02820620.
  6. Choudhuri, S.K.R. (2007), "On a thermoelastic three-phase-lag model", J. Therm. Stress., 30, 231-238. https://doi.org/10.1080/01495730601130919
  7. Eringen, A.C. and Suhubi, E.S. (1964), "Nonlinesr theory of simple micro-elastic solids-I", Int. J. Eng. Sci., 2(2), 189-203. https://doi.org/10.1016/0020-7225(64)90004-7
  8. Eringen, A.C. (1966), "Linear theory of micropolar elasticity", J. Appl. Math. Mech., 15, 909-924.
  9. Hobiny, A.D. and Abbas, I.A. (2020), "Fractional order thermoelastic wave assessment in a two-dimensional medium with voids", Geomech. Eng., 21(1), 85-93. https://doi.org/10.12989/gae.2020.21.1.085.
  10. Khurana, A. and Tomar, S.K. (2019), "Waves at interface of dissimilar nonlocal micropolar elastic half-spaces", Mech. Adv. Mater. Struct., 26(10). https://doi.org/10.1080/15376494.2018.1430261.
  11. Kumar, R. and Singh, B. (1996), "Wave propagation in a micropolar generalized thermoelastic body with stretch", Proc. Indian Acad. Sci., 106(2), 183 199.
  12. Kumar, R. and Rani, L. (2004), "Deformation due to mechanical and thermal sources in generalised orthorhombic thermoelastic material", Sadhana, 29, 429-447. https://doi.org/10.1007/BF02703254
  13. Kumar, R. and Deswal, S. (2001), "Mechanical and thermal sources in a micropolar generalized thermoelastic medium", J. Sound Vib., 239(3), 467-488. https://doi.org/10.1006/jsvi.2000.3143.
  14. Lata, P. and Zakhmi, H. (2019), "Fractional order thermoelasticity study in orthotropic medium of type GN-III", Geomech. Eng., 19(4), 295-305. https://doi.org/10.12989/gae.2019.19.4.295.
  15. Lata, P. and Kaur, H. (2020), "Effect of two temperature on isotropic modified couple stress thermoelastic medium with and without energy dissipation", Geomech. Eng., 21(5), 461-469. https://doi.org/10.12989/gae.2020.21.5.461.
  16. Marin, M.,Othman, M.I.A., Seadawy, A.R. and Carstea, C. (2020), "A domain of influence in the Moore-Gibson-Thompson theory of dipolar bodies", J. Taibah Univ. Sci., 14(1), 653-660. https://doi.org/10.1080/16583655.2020.1763664.
  17. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermo-elastic body with two temperatures", Abstract and Applied Analysis, 2013, Art. ID 583464, 1-7.
  18. Marin, M. (2010), "A domain of influence theorem for microstretch elastic materials", Nonlinear Anal.: R.W.A., 11(5), 3446-3452. https://doi.org/10.1016/j.nonrwa.2009.12.005.
  19. Noda, N. (1986), "Thermal stresses in materials with temperature-dependent properties", Thermal Stresses I, (Ed., R.B. Hetnarski), North-Holland, Amsterdam.
  20. Othman, M.I.A. and Singh, B. (2007), "The effect of rotation on generalized micropolar thermoelasticity for a half-space under five theories", Int. J. Solid. Struct., 44(9), 2748-2762. https://doi.org/10.1016/j.ijsolstr.2006.08.016.
  21. Othman, M.I.A. and Said, S.M. (2012), "The effect of rotation on two-dimensional problem of a fiber-reinforced thermoelastic with one relaxation time", Int. J. Thermophys., 33, 160-171. https://doi.org/10.1007/s10765-011-1109-5.
  22. Othman, M.I.A., Hasona, W.M. and Abd-Elaziz, E.M. (2014), "The effect of rotation on the problem of fiber-reinforced under generalized magneto-thermoelasticity subject to thermal loading due to laser pulse: A comparison of different theories", Can. J. Phys., 92(9), 1002-1015. https://doi.org/10.1139/cjp-2013-0321.
  23. Othman, M.I.A. and Song, Y.Q. (2009), "The effect of rotation on 2-D thermal shock problems for a generalized magneto-thermo-elasticity half-space under three theories", Multi. Model. Mater. Struct., 5(1), 43-58. https://doi.org/10.1108/15736105200900003.
  24. Othman, M.I.A. and Said, S.M. (2019), "Effect of gravity field and moving internal heat source on a 2-D problem of a fiber- reinforced thermoelastic medium: Comparison of different theories", Mech. Adv. Mater. Struct., 26(9), 796-804. https://doi.org/10.1080/15376494.2017.1410917.
  25. 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 three-phase-lag model", Int. J. Numer. Method. Heat Fluid Fl., 29(12), 4788-4806. https://doi.org/10.1108/HFF-04-2019-0359.
  26. Parfitt, V.R. and Eringen, A.C. (1969), "Reflection of plane wavesfrom a flat boundary of a micropolar elastic half-space", J. Acoust. Soc. Am., 45, 1258-1272 https://doi.org/10.1121/1.1911598
  27. Roy, I., Acharya, D.P. and Acharya, S. (2017), "Propagation and reflection of plane waves in a rotating magneto elastic fibre-reinforced semi space with surface stress", Mech. Mech. Eng., 21(4), 1043-1061.
  28. Said, S.M. and Othman, M.I.A. (2015), "Influence of the mechanical force and the magnetic field on fiber-reinforced medium for three-phase-lag model", Eur. J. Comp. Mech., 24(5) 210-231. http://dx.doi.org/10.1080/17797179.2015.1137751.
  29. Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model", Struct. Eng. Mech., 57(2), 201-220. http://doi.org/10.12989/sem.2016.57.2.201.
  30. Said, S.M. and Othman, M.I.A. (2020), "The effect of gravity and hydrostatic initial stress with variable thermal conductivity on a magneto-fiber-reinforced", Struct. Eng. Mech., 74(3), 425-434. https://doi.org/10.12989/sem.2020.74.3.001
  31. Sarkar, N. and Atwa, S.Y. (2019), "Two-temperature problem of a fiber-reinforced thermoelastic medium with a model-I crack under Green-Naghdi theory", Microsystem Technologies, 25, 1357-1367. https://doi.org/10.1007/s00542-018-4167-9.
  32. Sarkar, N. and Lahiri, A. (2013), "The effect of gravity field on the plane waves in a fiber-reinforced two-temperature magneto-thermoelastic medium under Lord-Shulman theory", J. Therm. Stress., 36, 895-914. https://doi.org/10.1080/01495739.2013.770709.
  33. Sarkar, N. (2014), "Analysis of magneto-thermoelastic response in a fiber-reinforced elastic solid due to hydrostatic initial stress and gravity field", J. Therm. Stress., 37(4), 387-404. https://doi.org/10.1080/01495739.2013.870845.
  34. Sarkar, N. and Atwa, S.Y. (2019), "Two-temperature problem of a fiber-reinforced thermoelastic mediumwith a Mode-I crack under GreenNaghdi theory", Microsys. Tech., 25(4), 1357-1367. https://doi.org/10.1007/s00542-018-4167-9.
  35. Sarkar, N. and Modal, S. (2019), "Transient responses in a two-temperature thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory-dependent derivative", ZAMM, 99(6), e201800343. https://doi.org/10.1002/zamm.201800343.
  36. Sarkar, N., Ghosh, D. and Lahiri, A. (2019), "A two-dimensional magneto-thermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative", Mech. Adv. Mater. Struct., 26(11), 957-966. https://doi.org/10.1080/15376494.2018.1432784.
  37. Sarkar, N. and Modal, S. (2020), "Two-dimensional problem of two-temperature generalized thermoelasticity using memory-dependent heat transfer: An integral transform approach", Ind. J. Phys., 94, 1965-1974. https://doi.org/10.1007/s12648-019-01639-9.
  38. Sengupta, P.R. and Nath, S. (2001), "Surface waves in fibre-reinforced anisotropic elastic media", Sadhana, 363-370.
  39. Verma, P.D.S. and Rana, O.H. (1983), "Rotation of a circular cylindrical tube reinforced by fibers lying along helices", Mech. Mater., 2(4), 353-359. https://doi.org/10.1016/0167-6636(83)90026-1.
  40. Xue, B., Xu, H., Fu, Z. and Sun, Q. (2010), "Reflection and refraction of longitudinal displacement wave at interface between two micropolar elastic solid", Adv. Mater. Res., 139-141, 214-217. https://doi.org/10.4028/www.scientific.net/AMR.139-141.214.
  41. Zhang, P., Wei, P. and Tang, Q. (2015), "Reflection of micropolar elastic waves at the non-free surface of a micropolar elastic half-space", Acta Mechanica, 226(9), 2925-2937. https://doi.org/10.1007/s00707-015-1346-y.
  42. Zhang, P., Wei, P., and Li, Y. (2017), "Reflection of longitudinal displacement wave at the visco-elastically supported boundary of micropolar half-space", Meccanica, 52(7), 1641-1654. https://doi.org/10.1007/s11012-016-0514-z.