Advances in materials Research

  • 제8권2호
  • /
  • Pages.83-102
  • /
  • 2019
  • /
  • 2234-0912(pISSN)
  • /
  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effect of inclined load on transversely isotropic magneto thermoelastic rotating solid with time harmonic source

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2019.05.15
  • 심사 : 2019.06.15
  • 발행 : 2019.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present research deals with the time harmonic deformation in transversely isotropic magneto thermoelastic solid with two temperature (2T), rotation and without energy dissipation due to inclined load. Lord-Shulman theory has been formulated for this mathematical model. The entire thermo-elastic medium is rotating with a uniform angular velocity. The 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 time harmonic source and rotation is depicted graphically on the resulting quantities.

키워드

참고문헌

  1. Abd-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
  2. Abd-alla, A.E.N.N., Alshaikh, F., Del Vescovo, D. and Spagnuolo, M. (2015), "Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity", New Developments Pure Appl. Math., 40(9), 1079-1092. https://doi.org/10.1080/01495739.2017.1334528
  3. Abo-Dahab, S.M., Jahangir, A. and Abo-el-nour, N. (2018), "Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation", Continuum Mech. Thermodyn., 1-13. https://doi.org/10.1007/s00161-018-0739-2
  4. 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. (English Edition) 30(12), 1505-1518. https://doi.org/10.1007/s10483-009-1203-6
  5. 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
  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. 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..13, 7505-7527.
  9. Chen, P.J. and Gurtin, M.E. (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
  10. 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
  11. Chen, P.J., Gurtin, M.E. and Williams, W.O. (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
  12. 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
  13. 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
  14. Ezzat, M.A. and El-Bary, A.A. (2017a), "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
  15. Ezzat, M.A. and El-Bary, A.A. (2017b), "Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307.
  16. 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", Nuclear Eng. Des., 252, 267- 277. https://doi.org/10.1016/j.nucengdes.2012.06.012
  17. Ezzat, M., El-Karamany, A. and El-Bary, A. (2015), "Thermo-viscoelastic materials with fractional relaxation operators", Appl. Math. Model., 39(23), 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018
  18. 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
  19. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017a), "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 El-Bary, A.A. (2017b), "Thermoelectric viscoelastic materials with memory-dependent derivative", Smart Struct. Syst., Int. J., 19(5), 539-577. http://dx.doi.org/10.12989/sss.2017.19.5.539
  21. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Thermal Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136
  22. Green, A.E. and Naghdi, P.M. (2017), "Thermoelasticity without energy dissipation", J. Phys. Math. , 31(3), 189-208. https://doi.org/10.1007/BF00044969
  23. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transform", J. Computat. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  24. 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., Int. J. 57(1), 91-103. http://dx.doi.org/10.12989/sem.2016.57.1.091
  25. 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.
  26. 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
  27. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (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
  28. 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.
  29. Lata, P. (2018), "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
  30. 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. https://doi.org/10.12989/csm.2019.8.1.055
  31. Lata, P. and Kaur, I. (2019b), "Study of transversely isotropic thick circular plate due to ring load with two temperature & green nagdhi theory of type-I, II and III", International Conference on Sustainable Computing in Science, Technology & Management (SUSCOM-2019), - Elsevier SSRN., Amity University Rajasthan, Jaipur, India, pp. 1753-1767.
  32. Lata, P. and Kaur, I. (2019c), "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
  33. 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
  34. Lata, P. and Kaur, I. (2019e), "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
  35. 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
  36. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  37. 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
  38. 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, 23(1), 171-184. https://doi.org/10.1515/auom-2015-0011
  39. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Revista de la Academia Canaria de Ciencias, 8(1), 101-106.
  40. Marin, M. (1997a), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mech., 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  41. Marin, M. (1997b), "On weak solutions in elasticity of dipolar bodies with voids", J. Computat. Appl. Math., 82(1-2), 291-297. https://doi.org/10.1016/S0377-0427(97)00047-2
  42. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Cienc. Mat. (Havana), 16(2), 101-109.
  43. Marin, M. (2008), "Weak solutions in elasticity of dipolar porous materials", Math. Problems Eng., 1-8. http://dx.doi.org/10.1155/2008/158908
  44. 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
  45. 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
  46. 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
  47. Marin, M. and Baleanu, D. (2016), "On vibrations in thermoelasticity without energy dissipation for micropolar bodies", Boundary Value Problems, 2016(1), 111. https://doi.org/10.1007/s11012-015-0265-2
  48. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continuum Mech. Thermodyn., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4
  49. Marin, M. and Ochsner, 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
  50. Marin, M. and Stan, G. (2013), "Weak solutions in Elasticity of dipolar bodies with stretch", Carpathian J. Math., 29(1), 33-40. https://doi.org/10.37193/CJM.2013.01.12
  51. 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
  52. 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
  53. 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
  54. Othman, M.I., Khan, A., Jahangir, R. and Jahangir, A. (2019), "Analysis on plane waves through magneto-thermoelastic microstretch rotating medium with temperature dependent elastic properties", Appl. Math. Model., 65, 535-548. https://doi.org/10.1016/j.apm.2018.08.032
  55. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1986), "Numerical recipes in Fortran 77", Cambridge University Press Cambridge.
  56. Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quarter. Appl. Math., 31, 115-125. https://doi.org/10.1090/qam/99708
  57. Sharma, J.N. and Kaur, D. (2010), "Rayleigh waves in rotating thermoelastic solids with voids", Int. J. Appl. Math. Mech., 6(3), 43-61. https://doi.org/10.1090/qam/99708
  58. 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.
  59. 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
  60. 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
  61. Slaughter, W.S. (2002), The Linearised Theory of Elasticity, Birkhausar.

피인용 문헌

  1. Transversely isotropic Euler Bernoulli thermoelastic nanobeam with laser pulse and with modified three phase lag Green Nagdhi heat transfer vol.40, pp.6, 2019, https://doi.org/10.12989/scs.2021.40.6.829