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Axisymmetric thermomechanical analysis of transversely isotropic magneto thermoelastic solid due to time-harmonic sources

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2019.07.15
  • Accepted : 2019.09.26
  • Published : 2019.10.25

Abstract

The present research deals with two-dimensional axisymmetric deformation in transversely isotropic magneto thermoelastic solid with and without energy dissipation, with two temperature and time-harmonic source. The proposed model is helpful for finding the type of relations between mechanical and thermal fields as most of the structural elements of heavy industries are frequently related to mechanical and thermal stresses at a higher temperature. The Hankel transform has been used to find a solution to the problem. The displacement components, stress components, and temperature distribution with the horizontal distance in the physical domain are calculated numerically. The effect of time-harmonic source and two temperature is depicted graphically on the resulting quantities.

Keywords

References

  1. Abbas, I.A. (2015), "The effects of relaxation times and a moving heat source on a two-temperature generalized thermoelastic thin slim strip", Can. J. Phys., 93(5), 585-590. https://doi.org/10.1139/cjp-2014-0387.
  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. https://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", Int. J. Thermophys., 33(7), 1302-1313. https://doi.org/10.1007/s10765-012-1272-3.
  4. Abbas, I.A., El-Amin, M.F. and Salama, A. (2009), "Effect of thermal dispersion on free convection in a fluid saturated porous medium", Int. J. Heat Fluid Flow, 30(2), 229-236. https://doi.org/10.1016/j.ijheatfluidflow.2009.01.004.
  5. Abd-Alla, A.E.N.N. and Alshaikh, F. (2015), "The mathematical model of reflection of plane waves in a transversely isotropic magneto-thermoelastic medium under rotation", New Dev. Pure Appl. Math., 282-289.
  6. Abd-Allaa, A. and Mahmoud, S.R. (2011), "Magneto-thermo-viscoelastic interactions in an unbounded nonhomogeneous body with a spherical cavity subjected to a periodic loading", Appl. Math. Sci., 5(29), 1431-1447.
  7. Abd-El-Salam, M., Abd-Alla, A. and Hosham, H. (2007), "Numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite-difference method", Appl. Math. Sci., 31(8), 1662-1670. https://doi.org/10.1016/j.apm.2006.05.009.
  8. Ailawalia, P., Kumar, S. and Pathania, D. (2010), "Effect of rotation in a generalized thermoelastic medium with two temperature under hydrostatic initial stress and gravity", Multidiscipline Model. Mater. Struct., 6(2), 185-205. https://doi.org/10.1108/15736101011067984.
  9. Argeso, H. and Eraslan, A. (2008), "On the use of temperaturedependent physical properties in thermomechanical calculations for solid and hollow cylinder", Int. J. Therm. Sci., 47(2), 136-146. https://doi.org/10.1016/j.ijthermalsci.2007.01.029.
  10. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 64(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  11. Atwa, S.Y. (2014), "Generalized magneto-thermoelasticity with two temperature and initial stress under Green-Naghdi theory", Appl. Math. Modell., 38(21-22), 5217-5230. https://doi.org/10.1016/j.apm.2014.04.023.
  12. Bijarnia, R. and Singh, B. (2016), "Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids", Int. J. Appl. Mech. Eng., 21(1), 285-301. https://doi.org/10.1515/ijame-2016-0018.
  13. Bouderba, B., Ahmed, H.M. adn Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  14. Chauthale, S. and Khobragade, N.W. (2017), "Thermoelastic response of a thick circular plate due to heat generation and its thermal stresses", Glob. J. Pure Appl. Math., 13, 7505-7527.
  15. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  16. Erbay, H., Erbay, S. and Dost, S. (1991), "Thermally induced vibrations in a generalized thermoelastic solid with a cavity", J. Therm. Stresses, 14(2), 161-171. https://doi.org/10.1080/01495739108927059.
  17. Ezzat, M. and AI-Bary, 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.
  18. Ezzat, M.A. and El-Bary, A.A. (2017), "A functionally graded magneto-thermoelastic half space with memory-dependent derivatives heat transfer", Steel Compos. Struct., 25(2), 177-186. http://doi.org/10.12989/scs.2017.25.2.177
  19. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017), "Two-temperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer", Microsyst. Technol., 24(2), 951-961. https://doi.org/10.1007/s00542-017-3425-6.
  20. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer", Nucl. Eng. Des., 252, 267-277. https://doi.org/10.1016/j.nucengdes.2012.06.012.
  21. Ezzat, M.A., Karamany, A.S. and El-Bary, A.A. (2017), "Thermoelectric viscoelastic materials with memory-dependent derivative", Smart Struct. Syst., 19(5), 539-551. http://doi.org/10.12989/sss.2017.19.5.539.
  22. Farhan, A.M., Abd-Alla, A.M. and Khder, M. A. (2019), "Solution of a problem of thermal stresses in a non-homogeneous thermoelastic infinite medium of isotropic material by finite difference method", J. Ocean Eng. Sci., https://doi.org/10.1016/j.joes.2019.05.001
  23. Hassan, M., Marin, M., Ellahi, R. and Alamri, S. (2018), "Exploration of convective heat transfer and flow characteristics synthesis by Cu-Ag/water hybrid-nanofluids", Heat Transfer Res., 49(18), 1837-1848. http://doi.org/10.1615/HeatTransRes.2018025569 .
  24. Hou, P.F., Luo, W. and Leung, A. (2008), "A point heat source on the surface of a semi-infinite transversely isotropic piezothermoelastic material", J. Appl. Mech., 75(1). http://doi.org/10.1115/1.2745402.
  25. Kaur, I. and Lata, P. (2019b), "Effect of hall current on propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer", SN Appl. Sci., 1(8), 900. https://doi.org/10.1007/s42452-019-0942-1.
  26. Kaur, I. and Lata, P. (2019f), "Transversely isotropic thermoelastic thin circular plate with constant and periodically varying load and heat source", Int. J. Mech. Mater. Eng., 14(10), 1-13. https://doi.org/10.1186/s40712-019-0107-4.
  27. Khalili, S.M., Mohazzab, A.H. and Jabbari, M. (2010), "Analytical solution for two-dimensional magneto-thermo-mechanical response in FG hollow sphere", Turk. J. Eng. Environ. Sci., 34(4), 231-252. https://doi.org/10.3906/muh-0909-40.
  28. Kordkheili, H.M., Amiri, G.G. and Hosseini, M. (2017), "Axisymmetric analysis of a thermoelastic isotropic half-space under buried sources in displacement and temperature potentials", J. Therm. Stresses, 40(2), 237-254. https://doi.org/10.1080/01495739.2016.1234342.
  29. Kumar, R., Sharma, N. and Lata, P. (2016a), "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.2016.57.1.091.
  30. Kumar, R., Sharma, N. and Lata, P. (2016b), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Modell., 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.
  31. Kumar, R., Sharma, N. and Lata, P. (2016d), "Effect of thermal and diffusion phase-lags in a thick circular plate with axisymmetric heat supply", Multidiscipline Modell. Mater. Struct., 12(2), 275-290. https://doi.org/10.1080/23311835.2015.1129811.
  32. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, A.S. (2017), "Rayleigh waves in anisotropic magnetothermoelastic medium", Coupled Syst. Mech., 6(3), 317-333. https://doi.org/10.12989/csm.2017.6.3.317.
  33. Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. http://ddoi.org/10.12989/scs.2018.27.4.439.
  34. Lata, P. (2019), "Time harmonic interactions in fractional Thermoelastic diffusive thick circular plate", Coupled Syst. Mech., 8(1), 39-53. https://doi.org/10.12989/csm.2019.8.1.039.
  35. Lata, P. and Kaur, I. (2019a), "Transversely isotropic thick plate with two temperature and GN type-III in frequency domain", Coupled Syst. Mech., 8(1), 55-70. http://doi.org/10.12989/csm.2019.8.1.055.
  36. Lata, P. and Kaur, I. (2019c), "Thermomechanical interactions in transversely isotropic thick circular plate with axisymmetric heat supply", Struct. Eng. Mech., 69(6), 607-614. http://doi.org/10.12989/sem.2019.69.6.607.
  37. Lata, P. and Kaur, I. (2019d), "Transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation in generalized thermoelasticity due to inclined load", SN Appl. Sci., 1(5), 426. https://doi.org/10.1007/s42452-019-0438-z.
  38. Lata, P. and Kaur, I. (2019e), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., 70(2), 245-255. http://doi.org/10.12989/sem.2019.70.2.245.
  39. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. http://dx.doi.org/10.12989/scs.2016.22.3.567.
  40. Mahmoud, S. (2012), "Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field", Meccanica, 47(7), 1561-1579. https://doi.org/10.1007/s11012-011-9535-9.
  41. Marin, M. (1997), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mechanica, 122(1-4), 155-168. https://doi.org/10.1007/BF01181996.
  42. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas(Havana), 16(2), 101-109.
  43. Marin, M. (1999), "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math. Phys., 40(3), 1391-1399. https://doi.org/10.1063/1.532809.
  44. Marin, M. (2016), "An approach of a heat flux dependent theory for micropolar porous media", Meccanica, 51(5), 1127-1133. https://doi.org/10.1007/s11012-015-0265-2.
  45. Marin, M. and Craciun, E. (2017), "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials", Compos. Part B Eng., 126, 27-37. https://doi.org/10.1016/j.compositesb.2017.05.063
  46. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermoelastic body with two temperatures", Abstract Appl. Anal., 1-7. http://doi.org/10.1155/2013/583464.
  47. Mohamed, R.A., Abbas, I.A. and Abo-Dahab, S. (2009), "Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction", Commun. Nonlin. Sci. Numer. Simul., 14(4), 1385-1395. https://doi.org/10.1016/j.cnsns.2008.04.006.
  48. Othman, M.I. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory", Results Phys., 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.012
  49. Press, W., Teukolshy, S.A., Vellerling, W.T. and Flannery, B. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge, U.K.
  50. Rehbinder, G. (1987), "Thermally induced vibrations in an elastic body with a spherical cavity", J. Therm. Stresses, 10, 307-317. https://doi.org/10.1080/01495738708927015.
  51. Shahani, A.R. and Torki, H.S. (2018), "Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity", Continuum Mech. Thermodyn., 30(3), 509-527. https://doi.org/10.1007/s00161-017-0618-2.
  52. Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22, 107-117.
  53. Singh, B. and Yadav, A.K. (2012), "Plane waves in a transversely isotropic rotating magnetothermoelastic medium", J. Eng. Phys. Thermophys., 85(5), 1226-1232. https://doi.org/10.1007/s10891-012-0765-z.
  54. Slaughter, W.S. (2002), The Linearized Theory of Elasticity, Birkhauser.
  55. Zenkour, A.M. and Abbas, I.A. (2014), A generalized thermoelasticity problem of an annular cylinder with temperature-dependent density and material properties, Int. J. Mech. Sci., 84, 54-60. https://doi.org/10.1016/j.ijmecsci.2014.03.016.

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