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Fractional effect in an orthotropic magneto-thermoelastic rotating solid of type GN-II due to normal force

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University Patiala) ;
  • Himanshi, Himanshi (Department of Basic and Applied Sciences, Punjabi University Patiala)
  • Received : 2021.07.20
  • Accepted : 2021.11.16
  • Published : 2022.02.25

Abstract

In this article, we have examined the effect of fractional order parameter in a two-dimensional orthotropic magneto-thermoelastic solid in generalized thermoelasticity without energy dissipation with fractional order heat transfer in the context of hall current, rotation and two-temperature due to normal force. Laplace and Fourier transform techniques are used to obtain the solution of the problem. The expressions for displacement components, stress components, current density components and conductive temperature are obtained in transformed domain and then in physical domain by using numerical inversion method. The effect of fractional parameter on all the components has been depicted through graphs. Some special cases are also discussed in the present investigation.

Keywords

References

  1. Abbas, I.A. (2011), "A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation", Sadhana, 36(3), 411-423. http://doi.org/10.1007/s12046-011-0025-5.
  2. Abbas, I.A. (2015), "Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity", Appl. Math. Model., 39(20), 6196-6206. https://doi.org/10.1016/j.apm.2015.01.065.
  3. Abbas, I.A. and Kumar, R. (2014), "Deformation due to thermal source in micropolar generalized thermoelastic half-space by finite element method", J. Comput. Theor. Nanosci., 11(1), 185-190. http://doi.org/10.1166/jctn.2014.3335.
  4. Abbas, I.A. and Marin, M. (2017), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Physica E: Low Dimens. Syst. Nanostr., 87, 254-260. http://doi.org/10.2016/j.physe.2016.10.048.
  5. Abbas, I.A., Alzahrani, F.S. and Elaiw, A. (2018), "A DPL model of photothermal interaction in a semiconductor material", Wav. Rand. Complex Media, 29(2), 328-343. https://doi.org/10.1080/17455030.2018.1433901.
  6. Abbas, I.A., Saeed, T. and Alhothuali, M. (2021), "Hyperbolic two-temperature photo-thermal interaction in a semiconductor medium with a cylindrical cavity", Silicon, 13(2), 1871-1878. http://doi.org/10.1007/s-12633-020-00570-7.
  7. Abd-Alla, A.M., Mahmoud, S.R. and Al-Shehri, N.A. (2011) "Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material", Appl. Math. Comput., 217(22), 8914-8922. http://doi.org/10.1016/j.amc.2011.03.077.
  8. Abd-Alla, A.M., Yahya, G.A. and Mahmoud, S.R. (2013a), "Effect of magnetic field and non-homogeneity on the radial vibrations in hollow rotating elastic cylinder", Meccanica, 48(3), 555-566. http://doi.org/10.1007/s11012-012-9615-5.
  9. Abd-Alla, A.M., Yahya, G.A. and Mahmoud, S.R. (2013b), "Radial vibrations in a non-homogeneous orthotropic elastic hollow sphere subjected to rotation", J. Comput. Theor. Nanosci., 10(2), 455-463. http://doi.org/10.1166/jctn.2013.2718.
  10. Abo-Dahab, S.M. and Abbas, I.A. (2011), "LS model on thermal shock problem of generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity", Appl. Math. Model., 35(8), 3759-3768. http://doi.org/10.1016/j.apm.2011.02.028.
  11. Abouelregal, E. (2019a), "Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat", Wav. Rand. Complex Media, 31(5), 812-832. http://doi.org/10.1080/17455030.2019.1628320.
  12. Abouelregal, E. (2019b), "Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two-phase-lags", Mater. Res. Exp., 6(11), 116535. https://doi.org/10.1088/2053-1591/ab447f
  13. Abouelregal, E. (2019c), "On Green and Naghdi thermoelasticity model without energy dissipation with higher order time differential and phase-lags", J. Appl. Comput. Mech., 6(3), 445-456. http://doi.org/10.22055/JACM.2019.29960.1649.
  14. Alharbi, A.M., Othman, M.I.A. and Atef, H.M. (2021) "Effect of viscosity and rotation on a generalized two-temperature thermoelasticity under five theories", Struct. Eng. Mech., 78(6), 755-764. http://doi.org/10.12989/sem.2021.78.6.755.
  15. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S.R., Adda Bedia, E.A. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. http://doi.org/10.12989/cac.2020.26.2.185.
  16. Alzahrani, F.S. and Abbas, I.A. (2016), "Effect of magnetic field on a thermoelastic fibre-reinforced material under GN-III theory", Steel Compos. Struct., 22(2), 369-386. http://doi.org/10.12989/scs.2016.22.2.369.
  17. Bakoura, A., Bourada, F., Bousahla, A.,Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. http://doi.org/10/12989/cac.2021.27.1.073. https://doi.org/10.12989/CAC.2021.27.1.073
  18. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. http://doi.org/10/12989/cac.2021.26.5.439. https://doi.org/10.12989/cac.2020.26.5.439
  19. Bellifa, H., Selim, M.M., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Al-Zahrani, M.M. and Tounsi, A. (2021), "Influence of porosity on thermal buckling behavior of functionally graded beams", Smart Struct. Syst., 27(4), 719-728. http://doi.org/10.12989/sss.2021.27.4.719.
  20. Bhatti, M.M., Ellahi, R., Zeeshan, A., Marin, M. and Ijaz, N. (2019), "Numerical study of heat transfer and Hall current impact on peristaltic propulsion of particle-fluid suspension with compliant wall properties", Modern Phys. Lett. B, 33(35), 1950439. http://doi.org/10.1142/S0217984919504396.
  21. Biswas, S. (2018), "Modelling of memory-dependent derivatives in orthotropic medium with three-phase-lag model under the effect of magnetic field", Mech. Bas. Des. Struct. Mach., 47(3), 302-318. http://doi.org/10.1080/15397734.2018.1548968.
  22. Biswas, S. and Abo-Dahab, S.M. (2020), "Electro-magneto-thermoelastic interactions in initially stressed orthotropic medium with Green-Naghdi model type-III", Mech. Bas. Des. Struct. Mach., 1-16. http://doi.org/10.1080/15397734.2020.1815212.
  23. Caputo, M. (1967), "Linear model of dissipation whose Q is always frequency independent-II", Geophys. J. Roy. Astron. Soc., 13, 529-539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x
  24. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 19(4), 614-627. https://doi.org/10.1007/BF01594969
  25. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on non-simple heat conduction", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 19(4), 969-970. https://doi.org/10.1007/BF01602278
  26. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 20(1), 107-112. https://doi.org/10.1007/BF01591120
  27. Ezzat, M.A. and EL-Bary, A.A. (2017), "Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. http://doi.org/10.12989/scs.2017.24.3.297.
  28. Guha, S. and Singh, A.K. (2021), "Frequency shifts and thermoelastic damping in different types of Nano/Microscale beams with sandiness and voids under three thermoelastic theories", J. Sound Vib., 510, 116301. http://doi.org/10.1016/j.jsv.2021.116301.
  29. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud S.R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. http://doi.org/10.12989/scs.2021.39.1.051.
  30. Hobiny, A. and Abbas, I.A. (2018), "Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material", Result. Phys., 10, 385-390. http://doi.org/10.1016/j.rinp.2018.06.035.
  31. Hobiny, A. and Abbas, I.A. (2021), "Generalized thermoelastic interaction in a two-dimensional orthotropic material caused by a pulse heat flux", Wav. Rand. Complex Media, 1-18. http://doi.org/10.1080/17455030.2021.1947543.
  32. Honig, G. and Hirdes, U. (1984), "A method for numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. http://doi.org/10.1016/0377-0427(84)90075-x.
  33. Kaur, H. and Lata, P. (2020), "Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures", Steel Compos. Struct., 34(2), 309-319. http://doi.org/10.12989/scs.2020.34.2.309.
  34. Kaur, I., Lata, P. and Singh, K. (2020), "Reflection of plane harmonic wave in rotating media with fractional order heat transfer", Adv. Mater. Res., 9(4), 289-309. http://doi.org/10.12989/amr.2020.9.4.289.
  35. Kumar, R. and Chawla, V. (2014), "General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids", Theor. Appl. Mech., 41(4), 247-265. http://doi.org/10.2298/TAM1404247.
  36. Kumar, R., Sharma, N. and Lata, P. (2016), "Effects of hall current in a transversely isotropic magnetothermoelastic with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. http://doi.org/10.12989/sem.2016.57.091.
  37. Kumar, R., Sharma, N. and Lata, P. (2017), "Effects of hall current and two temperature transversely isotropic magnetothermoelastic with and without energy dissipation due to ramp type heat", Mech. Adv. Mater. Struct., 24(8), 625-635. http://doi.org/10.1080/15376494.2016.1196769.
  38. Lata, P. and Himanshi. (2021a), "Orthotropic magnetothermoelastic solid with multi-dual-phase-lag model and hall current", Couple. Syst. Mech., 10(2), 103-121. http://doi.org/10.12989/csm.2021.10.2.103.
  39. Lata, P. and Himanshi. (2021b), "Stoneley wave propagation in an orthotropic thermoelastic media with fractional order theory", Compos. Mater. Eng., 3(1), 57-70. http://doi.org/10.12989/cme.2021.3.1.057.
  40. Lata, P. and Kaur, I. (2018), "Effect of hall current in transversely isotropic magneto-thermoelastic rotating medium with fractional order heat transfer due to normal force", Adv. Mater. Res., 7(3), 203-220. http://doi.org/10.12989/amr.2018.7.3.203.
  41. Lata, P. and Zakhmi, H. (2020), "Time harmonic interactions in an orthotropic media in the context of fractional order theory of thermoelasticity", Struct. Eng. Mech., 73(6), 725-735. http://doi.org/10.12989/sem.2020.73.6.725.
  42. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5.
  43. Marin, M. (1999) "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math. Phys., 40(3), 1391-1399. http://doi.org/10.1063/1.532809.
  44. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", AIP Adv., 5(3), 037113. http://doi.org/10.1063/1.4914912.
  45. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. http://doi.org/10.12989/scs.2021.39.5.631.
  46. Mudhaffar, M.I., Tounsi, A., Chikh, A., AL-Osta, M.A., Alzahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermomechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  47. Othman, M.I.A., Hasona, W.M. and Mansour, N.T. (2015), "Effect of magnetic field on generalized thermoelastic medium with two-temperature under three phase lag model", Multidisc. Model. Mater. Struct., 11(4), 544-557. http://doi.org/10.1108/MMMS-03-2015-0011.
  48. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, New York, NY, USA.
  49. Saeed, T., Abbas, I.A. and Marin, M. (2020), "A gl model on thermo-elastic interactions in a poroelastic material using finite element method", Symmetry, 12(3), 488. http://doi.org/10.3390/sym12030488.
  50. Sharma, N., Kumar, R. and Ram, P. (2008), "Dynamical behavior of generalized thermoelastic diffusion with two relaxation times in frequency domain", Struct. Eng. Mech., 28(1), 19-38. http://doi.org/10.12989/sem.2008.28.1.019.
  51. Shekhar, S. and Parvez, I.A. (2014), "Finite element analysis of the generalized magneto-thermoelastic in homogeneous orthotropic solid cylinder", International Conference on Mathematical Sciences, 257-260. http://doi.org/10.13140/2.1.4949.4403.
  52. Tahir, S.I., Chikh, A., Tounsi, A., AL-Osta, M.A., Al-Dulaijan, S.U. and Alzahrani, M.M. (2021b), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  53. Tahir, S.I., Tounsi, A., Chikh, A., AL-Osta, M.A., Al-Dulaijan, S.U. and Alzahrani, M.M. (2021a), "An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation", Wav. Rand. Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1942310.
  54. Youssef, H.M. (2006), "Theory of two temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. http://doi.org/10.1093/imamat/hxh101.
  55. Zenkour, A.M. (2018), "Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis", Acta Mechanica, 229(9), 3671-3692. https://doi.org/10.1007/s00707-018-2172-9.
  56. Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to timedependent heat flux", Steel Compos. Struct., 18(4), 909-924. http://doi.org/10.12989/scs.2015.18.4.909.
  57. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S.R. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. http://doi.org/10.12989/sem.2021.78.2.117.