Structural Engineering and Mechanics

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Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2019.01.16
  • Accepted : 2019.02.20
  • Published : 2019.04.25
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Abstract

In present research, we have considered transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation due to inclined load. The mathematical model has been formulated using Lord-Shulman theory. The Laplace and Fourier transform techniques have been used to find the solution to 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 using numerical inversion techniques. The effect of rotation and angle of inclination of inclined load is depicted graphically on the resulting quantities.

Keywords

References

  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 Develop. Pure Appl. Math., 282-289.
  2. Abouelregal, A.E. (2013), "Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat", Meccan., 48(7), 1731-1745. https://doi.org/10.1007/s11012-013-9705-z
  3. Ailawalia, P. and Narah, N.S. (2009), "Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid", Appl. Math. Mech., 30(12), 1505-1518. https://doi.org/10.1007/s10483-009-1203-6
  4. 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., 6(2), 185-205. https://doi.org/10.1108/15736101011067984
  5. Alla, A.M., Abo-Dahab, S.M. and Al-Thamali, T.A. (2012), "Propagation of Rayleigh waves in a rotating orthotropic material elastic half-space under initial stress and gravity", J. Mech. Sci. Technol., 26(9), 2815-2823. https://doi.org/10.1007/s12206-012-0736-5
  6. 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
  7. 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(2), 285-301. https://doi.org/10.1515/ijame-2016-0018
  8. Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quarter. Appl. Math., 38(1), 1-8. https://doi.org/10.1090/qam/575828
  9. 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. https://doi.org/10.12989/SCS.2017.25.2.177
  10. 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. https://doi.org/10.12989/sss.2017.19.5.539
  11. Ezzat, M. and El-Barrry, A.A. (2017), "Fractional magnetothermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. https://doi.org/10.12989/SCS.2017.24.3.297
  12. Gupta, R.R. and Gupta, R.R. (2014), "Effect of rotation on propagation of waves in transversely isotropic thermoelastic half-space", Ind. J. Mater. Sci., 1-7.
  13. Gupta, R. and Gupta, R. (2014), "Reflection of waves in a rotating transversely isotropic thermoelastic half-space under initial stress", J. Sol. Mech., 6(2), 229-239.
  14. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transform", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  15. Kumar, R. and Devi, S. (2011), "Deformation in porous thermoelastic material with temperature dependent properties", Appl. Math. Informat. Sci., 5(1), 132-147.
  16. Kumar, R. and Gupta, R.R. (2012), "Plane waves reflection in micropolar transversely isotropic generalized thermoelastic half-space", Math. Sci., 6(6), 1-10. https://doi.org/10.1186/2251-7456-6-1
  17. Kumar, R., Manthena, V.R., Lamba, N.K. and Kedar, G.D. (2017), "Generalized thermoelastic axi-symmetric deformation problem in a thick circular plate with dual phase lags and two temperatures", Mater. Phys. Mech., 32, 123-132.
  18. 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), 97-103.
  19. Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperatures and rotation", J. Sol. Mech., 8(4), 840-858.
  20. Kumar, R., Sharma, N. and Lata, P. (2016), "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
  21. Kumar, R., Sharma, N. and Lata, P. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. https://doi.org/10.12989/scs.2016.22.3.567
  22. 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
  23. Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. https://doi.org/10.12989/SCS.2018.27.4.439
  24. 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", Meccan., 47(7), 1561-1579. https://doi.org/10.1007/s11012-011-9535-9
  25. 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", 23(1), 171-184.
  26. Marin, M. (1997), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mech., 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  27. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermoelastic body with two temperatures", Abstr. Appl. Analy., 1-7.
  28. Marin, M. and O chsner, A. (2017), "The effect of a dipolar structure on the Holder stability in Green-Naghdi thermoelasticity", Contin. Mech. Thermodyn., 29(6), 1365-1374. https://doi.org/10.1007/s00161-017-0585-7
  29. Mona, K. and Se, K. (2017), "A problem in thermoelasticity with and without energy dissipation", J. Phys. Math., 8(3), 5.
  30. Press, W.T. (1986), Numerical Recipes in Fortran, Cambridge University Press Cambridge.
  31. Sharma, J.N. and Kaur, D. (2010), "Rayleigh Waves in rotating thermoelastic solids with voids", Int. J. Appl. Math. Mech., 6(3), 43-61.
  32. 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(2), 107-117.
  33. Shaw, S. and Mukhopadhyay, B. (2015), "Electromagnetic effects on wave propagation in an isotropic micropolar plate", J. Eng. Phys. Thermophys., 88(6), 1537-1547. https://doi.org/10.1007/s10891-015-1341-0
  34. Singh, B. and Yadav, A.K. (2012), "Plane waves in a Transversely isotropic rotating magnetothermoelastic medium", Eng. Phys. Thermophys., 85(5), 1226-1232. https://doi.org/10.1007/s10891-012-0765-z
  35. W.S, S. (2002), The Linearised Theory of Elasticity, Birkhausar.

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