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Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2019.04.25
  • 심사 : 2019.09.03
  • 발행 : 2019.09.25

초록

The purpose of this research paper is to depict the thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation in generalized LS theories of thermoelasticity. The Laplace and Fourier transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain numerically. The effect of two temperature and relaxation time are depicted graphically on the resulting quantities.

키워드

참고문헌

  1. 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 Developments Pure Appl. Math., 282-289.
  2. 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", Multidiscipl. Model. Mater. Struct. (Emerald), 6(2), 185-205. https://doi.org/10.1108/15736101011067984
  3. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  4. Banik, S. and Kanoria, M. (2012), "Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity", Appl. Math. Mech., 33(4), 483-498. https://doi.org/10.1007/s10483-012-1565-8
  5. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  6. Chauthale, S. and Khobragade, N.W. (2017), "Thermoelastic response of a thick circular plate due to heat generation and its thermal stresses", Global J. Pure Appl. Math., 7505-7527.
  7. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  8. Ezzat, M. and AI-Bary, A. (2016), "Magneto-thermoelectric viscoelastic materials with memory dependent derivatives involving two temperature", Int. J. Appl. Electromagnet. Mech., 50(4), 549-567. https://doi.org/10.3233/JAE-150131
  9. Ezzat, M. and AI-Bary, A. (2017), "Fractional magnetothermoelastic materials with phase lag Green-Naghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307. https://doi.org/10.12989/scs.2017.24.3.297
  10. 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., Int. J., 25(2), 177-186. https://doi.org/10.12989/scs.2017.25.2.177
  11. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Twotemperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer", Nuclear Eng. Des., 252, 267-277. https://doi.org/10.1016/j.nucengdes.2012.06.012
  12. Ezzat, M., El-Karamany, A. and El-Bary, A. (2015), "Thermoviscoelastic materials with fractional relaxation operators", Appl. Math. Model., 39(23), 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018
  13. Ezzat, M., El-Karamany, A. and El-Bary, A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23(5), 545-553. https://doi.org/10.1080/15376494.2015.1007189
  14. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017a), "Twotemperature 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
  15. Ezzat, M.A., Karamany, A.S. and El-Bary, A.A. (2017b), "Thermoelectric viscoelastic materials with memory-dependent derivative", Smart Struct. Syst., Int. J., 19(5), 539-551. https://doi.org/10.12989/sss.2017.19.5.539
  16. 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. https://doi.org/10.1615/HeatTransRes.2018025569
  17. Honig, G.H. and Hirdes, U. (1984), "A method for the inversion of Laplace Transform", J. Comput. Appl. Math,, 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  18. Kaur, I. and Lata, P. (2019a), "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, 900. https://doi.org/10.1007/s42452-019-0942-1
  19. Kaur, I. and Lata, P. (2019b), "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
  20. Kumar, R., Sharma, N. and Lata, A.P. (2016a), "Effects of Hall current in a transversely isotropic magnetothermoelastic with and without energy dissipation due to normal force", Struct. Eng. Mech., Int. J., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091
  21. Kumar, R., Sharma, N. and Lata, P. (2016b), "Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperatures and rotation", J. Solid Mech., 8(4), 840-858.
  22. Kumar, R., Sharma, N. and Lata, P. (2016c), "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. Model., 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  23. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, A.S. (2017), "Rayleigh waves in anisotropic magnetothermoelastic medium", Coupl. Syst. Mech., Int. J., 6(3), 317-333. https://doi.org/10.12989/csm.2017.6.3.317
  24. Kumar, R., Kaushal, P. and Sharma, R. (2018), "Transversely isotropic magneto-visco thermoelastic medium with vacuum and without energy dissipation", J. Solid Mech., 10(2), 416-434.
  25. Lata, P. (2018a), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., Int. J., 27(4), 439-451. https://doi.org/10.12989/scs.2018.27.4.439
  26. Lata, P. (2018b), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., Int. J., 66(1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113
  27. Lata, P. and Kaur, I. (2018), "Effect of hall current in Transversely Isotropic magnetothermoelastic rotating medium with fractional order heat transfer due to normal force", Adv. Mater. Res., Int. J., 7(3), 203-220. https://doi.org/10.12989/amr.2018.7.3.203
  28. Lata, P. and Kaur, I. (2019a), "Transversely isotropic thick plate with two temperature and GN type-III in frequency domain", Coupl. Syst. Mech., Int. J., 8(1), 55-70. http://dx.doi.org/10.12989/csm.2019.8.1.055
  29. Lata, P. and Kaur, I. (2019b), "Thermomechanical Interactions in Transversely Isotropic Thick Circular Plate with Axisymmetric Heat Supply", Struct. Eng. Mech., Int. J., 69(6), 607-614. http://dx.doi.org/10.12989/sem.2019.69.6.607
  30. Lata, P. and Kaur, I. (2019c), "Transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation in generalized thermoelasticity due to inclined load", SN Appl. Sci., 1, 426. https://doi.org/10.1007/s42452-019-0438-z
  31. Lata, P. and Kaur, I. (2019d), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., Int. J., 70(2), 245-255. http://dx.doi.org/10.12989/sem.2019.70.2.245
  32. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587. http://dx.doi.org/10.12989/scs.2016.22.3.567
  33. Lord, H.W. and Shulman, A.Y. (1967), "The Generalized Dynamical Theory of Thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  34. 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, 1561-1579. https://doi.org/10.1007/s11012-011-9535-9
  35. Mahmoud, S.R., Abd-Alla, A.M. and El-Sheikh, M.A. (2011), "Effect of the rotation on wave motion through cylindrical bore in a micropolar porous medium", Int. J. Modern Phys. B, 25(20), 2713-2728. https://doi.org/10.1142/S0217979211101739
  36. Mahmoud, S.R., Marin, M. and Al-Basyouni, K.S. (2015), "Effect of the initial stress and rotation on free vibrations in transversely isotropic human long dry bone", Analele Universitatii" Ovidius" Constanta-Seria Matematica, 171-184. https://doi.org/10.1142/S0217979211101739
  37. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Revista de la Academia Canaria de Ciencias, VIII, 8(1), 101-106.
  38. Marin, M. (1997), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mechanica, 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  39. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas (Havana), 16(2), 101-109.
  40. 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
  41. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Anal. Real World Appl., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001
  42. Marin, M. (2010), "A partition of energy in thermoelasticity of microstretch bodies", Nonlinear Anal.: Real World Appl., 11(4), 2436-2447. https://doi.org/10.1016/j.nonrwa.2009.07.014
  43. 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
  44. Marin, M. and O chsner, A. (2017), "The effect of a dipolar structure on the Holder stability in Green-Naghdi thermoelasticity", Continuum Mech. Thermodyn., 29, 1365-1374. https://doi.org/10.1007/s00161-017-0585-7
  45. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermoelastic body with two temperatures", Abstract Appl. Anal., 2013, 1-7. http://dx.doi.org/10.1155/2013/583464
  46. Marin, M., Craciun, E. and Pop, N. (2016), "Considerations on mixed initial-boundary value problems for micropolar porous bodies", Dyn. Syst. Appl., 25(1-2), 175-196.
  47. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpathian J. Math., 33(2), 219-232. https://doi.org/10.37193/CJM.2017.02.09
  48. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct. Int. J., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157
  49. Meradjah, M., Kaci, A., Houari, M.S., Tounsi, A. and Mahmoud, S. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  50. Othman, M. 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
  51. Press, W.T. (1986), Numerical Recipes in Fortran, Cambridge University Press Cambridge.
  52. Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quarterly Appl. Math., 31, 115-125. https://doi.org/10.1090/qam/99708
  53. 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.
  54. 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
  55. Slaughter, W.S. (2002). The Linearised Theory of Elasticity. Birkhausar.

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