Coupled systems mechanics

  • 제12권2호
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  • Pages.103-125
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  • 2023
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Plane harmonic waves in fractional orthotropic magneto-thermoelastic solid with rotation and two-temperature

  • Himanshi (Department of Mathematics, Punjabi University) ;
  • Parveen Lata (Department of Mathematics, Punjabi University)
  • 투고 : 2022.11.30
  • 심사 : 2023.03.20
  • 발행 : 2023.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present research is focused on the study of plane harmonic waves in a two-dimensional orthotropic magneto-thermoelastic media with fractional order theory of generalized thermoelasticity in the light of two-temperature and rotation due to time harmonic sources. Here, we studied three types of waves namely quasi-longitudinal (QL), quasi-transverse (QTS) and quasi thermal (QT) waves. The variations in the wave properties such as phase velocity, attenuation coefficient and specific loss have been noticed with respect to frequency for the reflected waves. Further the value of amplitude ratios, energy ratios and penetration depth are computed numerically with respect to angle of incidence. The numerical simulated results are presented graphically to show the effect of fractional parameter based on its conductivity (0<α<1 for weak, α=1 for normal, 1<α≤2 for strong conductivity) on all the components.

키워드

참고문헌

  1. 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.
  2. 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/s12633-020-00570-7.
  3. Abd-Alla, A.N. and Abbas, I.A. (2002), "A problem of generalized magneto-thermoelasticity for an infinitely long, perfectly conducting cylinder", J. Therm. Stress., 25(11), 1009-1025. https://doi.org/10.1080/01495730290074612.
  4. Abouelregal, A.E., Elhagary, M.A., Soleiman, A. and Khalil, K.M. (2020), "Generalized thermoelastic-diffusion model with higher-order fractional time derivatives and four-phase-lags", Mech. Bas. Des. Struct. Mach., 50(3), 897-914. http://doi.org/10.1080/15397734.2020.1730189.
  5. Bakoura, A., Djedid, I.K., Bourada, F., Bousahla, A.A., Mahmoud, S.R., Tounsi, A., ... & Alnujaie, A. (2022), "A mechanical behavior of composite plates using a simple three variable refined plate theory", Struct. Eng. Mech., 83(5), 617-625. https://doi.org/10.12989/sem.2022.83.5.617.
  6. Bhatti, M.M., Sait, S.M., Ellahi, R., Sheremet, M.A. and Oztop, H.F. (2022), "Thermal analysis of entropy generation of magnetic eyring-powell nanofluid with viscous dissipation in a wavy asymmetric channel", Int. J. Numer. Meth. Heat Fluid Flow, https://doi.org/10.1108/HFF-07-2022-0420.
  7. Bhatti, M.M., Shahid, A., Sarris, L.E. and Beg, O.A. (2023), "Spectral relaxation computation of Maxwell fluid flow from a stretching surface with quadratic convection and non-Fourier heat flux using Lie symmetry transformations", Int. J. Modern Phys. B, 37(9), 2350082. https://doi.org/10.1142/S0217979223500820.
  8. Biswas, S. and Abo-Dahab, S.M. (2018), "Effect of phase lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium", Appl. Math. Model., 59, 713-727. https://doi.org/10.1016/j.apm.2018.02.025.
  9. Borejko, P. (1996), "Reflection and transmission coefficients for three dimensional plane waves in elastic media", Wave Motion, 24(4), 371-393. https://doi.org/10.1016/S0165-2125(96)00026-1
  10. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F., ... & Mahmoud, SR. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821.
  11. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., ... & Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
  12. Chen, P.J. and Gurtin, E.M. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angewandte Mathematik und Physik, 19(4), 614-627. https://doi.org/10.1007/BF01594969
  13. Chen, P.J., Gurtin, E.M. and Williams, O.W. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", Zeitschrift fur angewandte Mathematik und Physik, 20(1), 107-112. https://doi.org/10.1007/BF01591120
  14. 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
  15. Das, P. and Kanoria, M. (2014), "Study of finite thermal waves in a magneto-thermoelastic rotating medium", J. Therm. Stress., 37(4), 405-428. https://doi.org/10.1080/01495739.2013.870847.
  16. Deswal, S. and Kalkal, K.K. (2014), "Plane waves in a fractional order micropolar magneto-thermoelastic half-space", Wave Motion, 51(1), 100-113. http://doi.org/10.1016/j.wavemoti.2013.06.009.
  17. Djilali, N., Bousahla, A.A., Kaci, A., Selim, M.M., Bourada, F., Tounsi, A., ... & Mahmoud, S.R. (2022), "Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT", Steel Compos. Struct., 42(6), 779-789. https://doi.org/10.12989/scs.2022.42.6.779.
  18. Ezzat, M.A. (2020), "Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties", J. Therm. Stress., 43(9), 1120-1137. http://doi.org/10.1080/01495739.2020.1770643.
  19. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & 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.
  20. Hebali, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & Tounsi, A. (2022), "Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model", Geomech. Eng., 28(1), 49-64. https://doi.org/10.12989/gae.2022.28.1.049.
  21. Hobiny, A.D. and Abbas, I.A. (2017), "A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity", Mech. Time Depend. Mater., 21(1), 61-72. https://doi.org/10.1007/s11043-016-9318-8.
  22. Kaur, R., Lata, P. and Singh, K. (2021), "Reflection of plane harmonic wave in rotating media with fractional order heat transfer and two temperature", Part. Diff. Equ. Math., 4, 100049. https://doi.org/10.1016/j.pdiff.2021.100049.
  23. Kaushal, S., Sharma, N. and Kumar, R. (2010), "Propagation of waves in generalized thermoelastic continua with two-temperature", Int. J. Appl. Mech. Eng., 15(4), 1111-1127.
  24. Khamis, A.K., Abdel Allah Nasr, A.M., EL-Bary, A.A. and Atef, H.M. (2021), "Effect of modified ohm's and Fourier's laws on magneto thermo-viscoelastic waves with Green-Naghdi theory in a homogeneous isotropic hollow cylinder", Int. J. Adv. Appl Sci., 8(6), 40-47. http://doi.org/10.1833/ijaas.2021.06.005.
  25. Kouider, D., Kaci, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., ... & Hussain, M. (2021), "An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core", Steel Compos. Struct., 41(2), 167-191. http://doi.org/10.12989/scs.2021.41.2.167.
  26. 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.
  27. Kumar, R. and Gupta, V. (2013), "Plane wave propagation in an anisotropic thermoelastic medium with fractional order derivative and void", J. Thermoelast., 1(1), 21-34.
  28. Lata, P. and Himanshi. (2021a), "Orthotropic magneto-thermoelastic 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
  29. Lata, P. and Himanshi. (2021b), "Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain", Struct. Eng. Mech., 77(3), 315-327. http://doi.org/10.12289/sem.2021.77.3.315.
  30. Lata, P. and Himanshi. (2021c), "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.
  31. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. http://doi.org/10.12989/scs.2016.22.3.567.
  32. Marin, M., Codarcea, L. and Chirila, A. (2017), "Qualitative results on mixed problem of micropolar bodies with microtemperatures", Appl. Appl. Math., 12(2), 776-789.
  33. Marin, M., Chirila, A. and Othman, M.I.A. (2019), "An extension of Dafermos's results for bodies with a dipolar structure", Appl. Math. Comput., 361, 680-688. https://doi.org/10.1016/j.amc.2019.06.024.
  34. Merazka et al. (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.
  35. Othman, M.I.A., Khan, A., Jahangir, R. and Jahangir, A. (2019b), "Analysis on plane waves through magneto-thermoelastic microstretch rotating medium with temperature dependent elastic properties", Appl. Math. Model., 65, 535-548. http://doi.org/10.1016/j.apm.2018.08.032.
  36. Othman, M.I.A., Said, S. and Marin, M. (2019a), "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. Meth. Heat Fluid Flow, 29(12), 4788-4806. http://doi.org/10.1108/HFF-04-2019-0359.
  37. Sharma, K. and Bhargava, R.R. (2014), "Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermoelastic solid", Afrika Mathematica, 25(1), 81-102. https://doi.org/10.1007/s13370-012-0099-1.
  38. Sharma, K. and Kumar, P. (2013), "Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids", J. Therm. Stress., 36(2), 94-111. https://doi.org/10.1080/01495739.2012.720545.
  39. Singh, B. and Singh, A. (2021), "Reflection of plane waves from the boundary of a thermo-magneto-electroelastic solid half space", Couple. Syst. Mech., 10(2), 143-159. http://doi.org/10.12989/csm.2021.10.2.143.
  40. Sinha, S.B. and Elsibai, K.A. (1997), "Reflection and refraction of thermoelastic waves at an interface of two semi-in finite media with two relaxation times", J. Therm. Stress., 20(2), 129-145. https://doi.org/10.1080/01495739708956095.
  41. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT", Steel Compos. Struct., 42(4), 501-511. https://doi.org/10.12989/scs.2022.42.4.501.
  42. Vinh, P.V. and Tounsi, A. (2022), "Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters", Thin Wall. Struct., 174, 109084. https://doi.org/10.1016/j.tws.2022.109084.
  43. Vinh, P.V. Chinh, N.V. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech., 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743.
  44. 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.
  45. Zakaria, M. (2014), "Effect of hall current on generalized Magneto-thermoelasticity micropolar solid subject to ramp type heating", Appl. Mech., 50(1), 92-104. https://doi.org/10.1007/s10778-014-0615-0.
  46. Zhang, L., Bhatti, M.M., Marin, M. and Mekheimer, K.S. (2020), "Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles", Entropy, 22(10), 1070. http://doi.org/10.3390/e22101070.