Structural Engineering and Mechanics

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Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University Patiala) ;
  • Himanshi, Himanshi (Department of Basic and Applied Sciences, Punjabi University Patiala)
  • Received : 2020.07.28
  • Accepted : 2020.10.31
  • Published : 2021.02.10
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Abstract

Here, in this research we have studied a two dimensional problem in a homogeneous orthotropic magneto-thermoelastic medium with higher order dual-phase-lag heat transfer with combined effects of rotation and hall current in generalized thermoelasticity due to time harmonic sources. As an application the bounding surface is subjected to uniformly distributed and concentrated loads (mechanical and thermal source). Fourier transform technique is used to solve the problem. The expressions for displacement components, stress components and temperature change are derived in frequency domain. Numerical inversion technique has been used to obtain the results in physical domain. The effect of frequency has been depicted with the help of graphs.

Keywords

References

  1. Abbas I. A. (2006), "Natural frequencies of a poroelastic hollow cylinder", Acta Mechanica, 186(1-4), 229-237. http://doi.org/10.1007/s00707-006-0314-y.
  2. Abbas, I. A. and Youssef H. M. (2009), "Finite element analysis of two-temperature generalized magneto-thermoelasticity", Arch. Appl. Mech., 79(10), 917-925. http://doi.org/10.1007/s00419-008-0259-9.
  3. Abbas I. A. and Youssef H. M. (2012), "A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method", J. Thermophys., 33(7), 1302-1313. https://doi.org/10.1007/s10765-012-1272-3
  4. Abbas, I.A. (2018a), "A study on fractional order theory in thermoelastic half-space under thermal loading", Physical Mesomechanics., 21(2), 150-156. https://doi.org/10.1134/S102995991802008X
  5. Abbas, I.A. (2018b), "Free vibrations of nanoscale beam under two-temperature Green Naghdi model", J. Acoustics Vib., 23(3), 289-293.http://doi.org/10.20855/ijav.2018.23.31051.
  6. 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
  7. 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
  8. 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. Theoretical Nanosci., 10(2), 455-463.http://doi.org/10.1166/jctn.2013.2718
  9. Abouelregal A. E. (2019a), "Rotating magneto-thermoelastic rod with finite length due to moving heat sources via Eringen's nonlocal model", J. Comput. Appl. Mech., 50(1), 118-126.http://doi.org/10.22059/JCAMECH.2019.275893.360
  10. Abouelregal A. E. (2019b), "A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags", Multidiscipline Model Mater. Struct., 16(4), 689-711. https://doi.org/10.1108/MMMS-07-2019-0138
  11. Abouelregal A. E. (2020), "A novel model of nonlocal thermoelasticity with time derivatives of higher order", Math. Methods Appl. Sci., http://doi.org/10.1002/mma.6416.
  12. Abouelregal E. (2019c), "Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat", Waves Random Complex Media, http://doi.org/10.1080/17455030.2019.1628320, 2019.
  13. Abouelregal E. (2019d), "Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two phase-lags, Materials Research Express, 6(11), 116535. https://doi.org/10.1088/2053-1591/ab447f.
  14. Abouelregal, E. (2019e), "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.
  15. Al-Basyouni, K.S., Mahmoud, S.R. and Alzahrani, E. (2014), "Effect of rotation, magnetic field and a periodic loading on radial vibrations thermo viscoelastic non-homogeneous media", Boundary Value Problems, 1(166), http://doi.org/10.1186/s1366-014-0166-7.
  16. Alzahrani, F.S. and Abbas, I.A. (2020), "Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model", Mathematics, 8(585), 1-11. http://doi.org/10.3390/math8040585.
  17. Biot, M.A. (1965), "Theory of stress-strain relations in an isotropic viscoelasticity, and relaxation phenomena", J. Appl. Phys., 18, 27-34. https://doi.org/10.1063/1.1697551
  18. Biswas, S., Mukhopadhyay, B. and Shaw, S. (2017), "Rayleigh surface wave propagation in orthotropic thermoelastic solid under three phase lag model", J. Thermal. Stress., 40(4), 403-419.http://doi.org/10.1080/01495739.2017.1283971.
  19. 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. Modelling, 59, 713-727.https://doi.org/10.1016/j.apm.2018.02.025.
  20. Biswas, S. (2018), "Modelling of memory-dependent derivatives in orthotropic medium with three-phase-lag model under the effect of magnetic field", Mech. Based Design Struct. Machines, 47(3), 302-318.http://doi.org/10.1080/15397734.2018.1548968.
  21. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166.https://doi.org/10.12989/cac.2020.25.2.155.
  22. Bourada, F., Bousahla, A.A., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, 25(6), 485-495.https://doi.org/10.12989/cac.2020.25.6.485.
  23. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, S.R. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487.https://doi.org/10.12989/gae.2020.21.5.471.
  24. Das, B. and Lahiri, A. (2015), "Generalized Magneto-thermoelasticity for isotropic media", J. Thermal. Stress., 38, 210-228. https://doi.org/10.1080/01495739.2014.985564
  25. Tzou, D.Y. (1995), "A unified field approach for heat conduction from macro to micro scales", J. Heat Transfer, 117(1), 8-16. http://doi.org/10.1115/1.2822329.
  26. EL-Naggar, A.M., Kishka, Z., Abd-Alla, A. and Abbas, I.A. (2013), "On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity", J. Comput. Theoretical Nanosci., 10(6), 1408-1417.http://doi.org/10.1166/jctn.2013.2862
  27. Ezzat, M.A. (2020), "Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties", J. Thermal Stress., 43(9), 1120-1137.http://doi.org/10.1080/01495739.2020.1770643
  28. Ezzat, M.A., EL- Karamany, A.S. and EL-Bary, A.A. (2014), "Magneto-thermoelasticity with two fractional order heat transfer", J. Association Arab U Basic Appl. Sci., http://dx.doi.org/10.1016/j.jau.bas.2014.06.009
  29. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elasticity, 31, 189-208. https://doi.org/10.1007/BF00044969
  30. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  31. Kumar, R. and Chawla, V. (2014), "General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids", Theoretical Appl. Mech., 41(4), 247-265. http://doi.org/ 10.2298/TAM1404247.
  32. Kumar, R., Sharma, N. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperature and without energy dissipation", Mater. Phys. Mech., 22(2), 107-117.
  33. Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magneto-thermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Modelling, 40(13-14), 6560-6575.http://doi.org/10.1016/j.apm.2016.01.061.
  34. Kumar, R., Sharma, N. and Lata, P. (2017)," Effects of hall current and two temperature transversely isotropic magneto-thermoelastic 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.
  35. Lata, P. (2019), "Time harmonic interactions in fractional thermoelastic diffusive thick circular plate", Coupled Syst. Mech., 8(1) 39-53. http://doi.org/10.12989/csm.2019.8.1.039.
  36. Lata, P. and Kaur, I. (2019), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Structural Engineering and Mechanics, 70(2), 245-255.http://doi.org/10.12289/sem.2019.70.2.245.
  37. Lata, P. and Zakhmi, H. (2019), "Fractional order generalized thermoelastic study in orthotropic medium of type GN-III, Geomech. Eng., 19(4), 295-305, http://doi.org/10.12989/gae.2019.19.4.295.
  38. Lata, P. and Zakhmi, H. (2020), "Time harmonic interactions in an orthotropic media in the context of fractional order theory of thermoelasticity", Structural Engineering and Mechanics, 73(6), 725-735.http://doi.org/10.12989/sem.2020.73.6.725.
  39. Lord, H.W., Shulman, Y. (1967), "A generalized dynamical theory of thermo-elasticity", J. Mech. Phys. Solids, 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  40. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", International Journal of Engineering Science, 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5
  41. Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes Rendus De Lacademie Des Sciences Serie II Fascicule B-Mecanique Physique Astronomie, 321(12), 375-480.
  42. Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control, 16(1), 33-47. https://doi.org/10.1177/1077546309103419
  43. Mashat, D.S., Zenkour, A.M. and Abouelregal, A.E. (2017), "Thermoelastic interactions in a rotating infinite orthotropic elastic body with a cylindrical hole and variable thermal conductivity", Arch. Mech. Eng., 64(4), 481-498.http://doi.org/10.1515/meceng-2017-0028.
  44. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Adda Bedia, E.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305.https://doi.org/10.12989/anr.2020.8.4.293.
  45. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2020), "A four-unknown refined plate theory for dynamicanalysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36(3), 355-367.http://dx.doi.org/10.12989/scs.2020.36.3.355
  46. Othman, M. I. A. and Song, Y. (2011), "Reflection of Magneto-thermoelastic waves from a rotating elastic half space in generalized thermoelasticity under three theories", Mech. Mech. Eng., 15(1), 5-24. https://doi.org/10.1016/j.ijengsci.2007.12.004.
  47. Othman, M. I. A. and Mansoure, N. (2015), "The effect of magnetic field on generalized thermoelastic medium with two temperature under three phase lag model", Multidiscipline 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), Fortran Numerical Recipes, Cambridge University Press, Cambridge, United Kingdom.
  49. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2). 119-132.https://doi.org/10.12989/gae.2020.22.2.119
  50. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244.https://doi.org/10.12989/cac.2020.25.3.225
  51. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermomechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325.https://doi.org/10.12989/cac.2020.25.4.311
  52. Roychoudhuri, S. K. and Bandyopadhyay, N. (2005), "Magneto-thermoelastic waves in a perfectly conducting elastic half space in thermoelasticity III", J. Math. Math. Sci., 20, 3303-3318. http://doi.org/10.1155/IJMMS.2005.3303.
  53. Saeed T. and Abbas, I. A. (2019), "Thermomechanical response in a two dimension porous medium subjected to thermal loading", J. Numerical Methods Heat Fluid Flow, 22(8), http://doi.org/10.1108/HFF-11-2019-0803.
  54. Saeed T., Abbas, I. A. and Marin M. (2019), "GL model on thermo-elastic interaction in a poroelastic material using finite element method", Symmetry, 12(3), 488. http://doi.org/10.3390/sym12030488.
  55. Schoenberg M. and Censor D. (1973), "Elastic waves in rotating media", Quarterly Appl. Math., 31, 115-125. https://doi.org/10.1090/qam/99708
  56. Sharma K. and Marin M. (2014), "Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids", Analele Universitatii Ovidius Constanta-Seria Mathematica, 22(2), 151-176. http://doi.org/10.2478/auom-2014-0040.
  57. Shekhar S. and Parvez I. A. (2014), "Finite element analysis of the generalized magneto-thermoelastic in homogeneous orthotropic solid cylinder", Conference Math. Sci., 257-260. http://doi.org/10.13140/2.1.4949.4403.
  58. 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. https://doi.org/10.12989/sem.2008.28.1.019
  59. Zenkour, A.M. (2020), "Magneto-thermal shock for a fiber-reinforced anisotropic half-space studied with a refined multi-dual-phase-lag model", J. Phys. Chem. Solids, 137, https://doi.org/10.1016/j.jpcs.2019.109213
  60. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. http://dx.doi.org/10.12989/cac.2020.26.1.063.