Coupled systems mechanics

  • 제8권1호
  • /
  • Pages.39-53
  • /
  • 2019
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Time harmonic interactions in fractional thermoelastic diffusive thick circular plate

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2018.09.10
  • 심사 : 2018.12.20
  • 발행 : 2019.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

Here in this investigation, a two-dimensional thermoelastic problem of thick circular plate of finite thickness under fractional order theory of thermoelastic diffusion has been considered in frequency domain. The effect of frequency in the axisymmetric thick circular plate has been depicted. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature change and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect frequency has been shown on the various components.

키워드

참고문헌

  1. Abbas, I.A. and Kumar, R. (2015), "Deformation in three dimensional thermoelastic medium with one relaxation time", J. Comput. Theoret. Nanosci., 12(10), 3104-3109. https://doi.org/10.1166/jctn.2015.4086
  2. Abbas, I.A., Kumar, R. and Rani, L. (2015), "Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating", Appl. Math. Comput., 254, 360-369. https://doi.org/10.1016/j.amc.2014.12.111
  3. Abbas, I.A., Marin, M. and Kumar, R. (2015), "Analytical-numerical solution of thermoelastic interactions in a semi- infinite medium with one relaxation time", J. Comput. Theoret. Nanosci., 12(2), 287-291. https://doi.org/10.1166/jctn.2015.3730
  4. Biswas, R.K. and Sen, S. (2011), "Fractional optimal control problems: A pseudo state-space approach", J. Vibr. Contr., 17(7), 1034-1041. https://doi.org/10.1177/1077546310373618
  5. Caputo, M. (1967), "Linear model of dissipation whose Q is always frequency independent", Geophys. J. Roy. Astronomic. Soc., 13, 529-539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x
  6. Debnath, L. (1995), Integral Transform and Their Applications, CRC Press Boca Raton.
  7. Ezzat, M.A. (2011a), "Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer", Phys. B, 406(1), 30-35. https://doi.org/10.1016/j.physb.2010.10.005
  8. Ezzat, M.A. (2011b), "Theory of fractional order in generalized thermoelectric MHD", Appl. Math. Model., 35(10), 4965-4978. https://doi.org/10.1016/j.apm.2011.04.004
  9. Ezzat, M.A. and Ezzat, S. (2016), "Fractional thermoelasticity applications for porous asphaltic materials", Petroleum Sci., 13(3), 550-560. https://doi.org/10.1007/s12182-016-0094-5
  10. Ezzat, M.A. and EI-Bary. (2016), "Modelling of fractional magneto-thermoelasticity for a perfect conducting materials", Smart Struct. Syst., 18(4), 701-731.
  11. Ezzat, M.A. and Fayik, M.A. (2011), "Fractional order theory of thermoelastic diffusion", J. Therm. Stress., 34, 851-872. https://doi.org/10.1080/01495739.2011.586274
  12. Jiang, X. and Xu, M. (2010), "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems", Phys. A, 389(17), 3368-3374. https://doi.org/10.1016/j.physa.2010.04.023
  13. Kumar, R., Sharma, N. and Lata, P. (2016), "Effect of thermal and diffusion phase lags in a thick circular plate due to a ring load with axisymmetric heat supply", Appl. Appl. Math., 11(2), 748-765.
  14. Kumar, R., Sharma, N. and Lata, P. (2016a), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091
  15. Kumar, R. and Sharma, P. (2017), "The effect of fractional order on energy ratios at the boundary surface of piezothermoelastic medium", Coupled Syst. Mech., 6(2), 175-187. https://doi.org/10.12989/CSM.2017.6.2.175
  16. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017), "Rayleigh waves in anisotropic magneto thermoelastic medium", Coupled Syst. Mech., 6(3), 317-333. https://doi.org/10.12989/CSM.2017.6.3.317
  17. Lata, P. (2018), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124. https://doi.org/10.12989/SEM.2018.66.1.113
  18. Lata, P. (2018a), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(2), 439-451. https://doi.org/10.12989/SCS.2018.27.4.439
  19. Marin, M. and Oechsner, 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
  20. Marin, M.(2013), "Weak solutions in elasticity of dipolar bodies with stretch", Carpath. J. Mech., 29(1), 33-40. https://doi.org/10.37193/CJM.2013.01.12
  21. Marin, M.(1997), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mech., 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  22. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermo-elastic body with two temperatures", Abstr. Appl. Analy., 2013, 583464.
  23. Mahmoud, S.R.(2016), "An analytical solution for the effect of initial stress, rotation, magnetic field and a periodic loading in a thermoviscoelastic medium with a spherical cavity", Mech. Adv. Mater. Struct., 23(1), 1-7. https://doi.org/10.1080/15376494.2014.884659
  24. Miller, K.S. and Ross, B. (1993), An Introduction to the Fractional Integrals and Derivatives-Theory and Applications, John Wiley and Sons Inc., New York, U.S.A.
  25. Povstenko, Y.Z. (2005), "Fractional heat conduction equation and associated thermal stresses", J. Therm. Stress., 28(1), 83-102. https://doi.org/10.1080/014957390523741
  26. Povstenko, Y.Z. (2009), "Thermoelasticity that uses fractional heat conduction equation", J. Math. Stress., 162(2), 296-305.
  27. Povstenko, Y.Z. (2010), "Fractional radial heat conduction in an infinite medium with a cylindrical cavity and associated thermal stresses", Mech. Res. Commun., 37(4), 436-440. https://doi.org/10.1016/j.mechrescom.2010.04.006
  28. Povstenko, Y.Z. (2011), "Fractional catteneo-type equations and generalized thermoelasticity", J. Therm. Stress., 34(2), 97-114. https://doi.org/10.1080/01495739.2010.511931
  29. Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vatterling, W.A. (1986), Numerical Recipes, Cambridge University Press, Cambridge, The Art of Scientific Computing.
  30. Tripathi, J.J., Kedar, G.D. and Deshmukh, K.C. (2015), "Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply", Acta Mech., 226(7), 2121-2134. https://doi.org/10.1007/s00707-015-1305-7
  31. Tripathi, J.J., Warbhe, S., Deshmukh, K.C. and Verma, J. (2018), "Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source", Multidiscipl. Model. Mater. Struct., 14(1), 2-15. https://doi.org/10.1108/MMMS-04-2017-0022
  32. Xiong, C. and Niu, Y. (2017), "Fractional order generalized thermoelastic diffusion theory", Appl. Math. Mech., 38(8), 1091-1108. https://doi.org/10.1007/s10483-017-2230-9
  33. Ying, X.H. and Yun, J.X. (2015), "Time fractional dual-phase-lag heat conduction equation", Chin. Phys. B, 24(3), 034401.
  34. Youssef, H.M. (2006), "Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating", Eur. J. Mech./Sol., 25(5), 745-763. https://doi.org/10.1016/j.euromechsol.2005.11.005
  35. Youssef, H.M. (2010), "Theory of fractional order generalized thermoelasticity", J. Heat Transf., 132(6), 1-7. https://doi.org/10.1115/1.4000705
  36. Zenkour, A.M. and Abbas, I.A. (2014), "Thermal shock problem for a fiber-reinforced anisotropic halfspace placed in a magnetic field via GN model", Appl. Math. Comput., 246, 482-490. https://doi.org/10.1016/j.amc.2014.08.052

피인용 문헌

  1. Thermomechanical response in a two-dimension porous medium subjected to thermal loading vol.30, pp.8, 2020, https://doi.org/10.1108/hff-11-2019-0803
  2. Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain vol.77, pp.3, 2019, https://doi.org/10.12989/sem.2021.77.3.315