Geomechanics and Engineering

  • 제19권5호
  • /
  • Pages.369-381
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  • 2019
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Harpreet (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2019.07.05
  • 심사 : 2019.11.11
  • 발행 : 2019.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

키워드

과제정보

The corresponding author Harpreet Kaur duly acknowledges the Junior Research Fellowship(JRF) received from University Grants Commission (UGC),Delhi India for pursuing her Ph.D. under the sanctioned no. 19/6/2016/(i) EU-V.

참고문헌

  1. Abbas I.A. (2016), "Free vibration of a thermoelastic hollow cylinder under two-temperature generalized thermoelastic theory", Mech. Based Des. Struct. Machines, 45(3), 395-405. https://doi.org/10.1080/15397734.2016.1231065.
  2. Abbas, I.A. (2014), "Three-phase lag model on thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity", J. Comput. Theor. Nanosci., 11(4), 987-992. https://doi.org/10.1166/jctn.2014.3454.
  3. Abbas, I.A. (2014c), "Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory", J. Mech. Sci. Technol., 28(10), 4193-4198. https://doi.org/10.1007/s12206-014-0932-6.
  4. Abbas, I.A. (2015), "A dual phase lag model on thermoelastic interaction in an infinite fiber reinforced anisotropic medium with a circular hole", Mech. Based Des. Struct. Machines, 43(4), 501-513. https://doi.org/10.1080/15397734.2015.1029589.
  5. Abbas, I.A. and Youssef, H.M. (2009), "Finite element analysis of two-temperature generalized magnetothermoelasticity", Arch. Appl. Mech., 79, 917-925. https://doi.org/10.1007/s00419-008-0259-9.
  6. Abbas, I.A. and Zenkour, A.M. (2014a), "Two-temperature generalized thermoelastic interaction in an infinite fiberreinforced anisotropic plate containing a circular cavity with two relaxation times", J. Comput. Theor. Nanosci., 11 (1), 1-7. https://doi.org/10.1166/jctn.2014.3309.
  7. Ansari, R., Ashrafi, M.A. and Hosseinzadeh, S. (2014), "Vibration characteristics of piezoelectric microbeams based on the modified couple stress theory", Shock Vib., 2014(1), 1-12. http://dx.doi.org/10.1155/2014/598292.
  8. Arif, S.M., Biwi, M. and Jahangir, A. (2018) "Solution of algebraic lyapunov equation on positive-definite hermitian matrices by using extended Hamiltonian algorithm", Comput. Mater. Continua, 54, 181-195.
  9. Atanasov, M.S., Karlicic, D., Kozic, P. and Janevski, G. (2017), "Thermal effect on free vibration and buckling of a doublemicrobeam system", Facta Universitatis Ser. Mech. Eng., 15(1), 45-62. https://doi.org/10.22190/FUME161115007S.
  10. Chen, W. and Li, X. (2014), "A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model", Arch. Appl. Mech., 84(3), 323-341. https://doi.org/10.1007/s00419-013-0802-1.
  11. Chen, W., Yang, S. and Li, X. (2014), "A study of scale effect of composite laminated plates based on new modified couple stress theory by finite-element method", J. Multiscale Comput. Eng., 12(6), 507-527. https://doi.org/10.1615/IntJMultCompEng.2014011286.
  12. Cosserat, E. and Cosserat, F. (1909), Theory of Deformable Bodies, Hermann et Fils, Paris, France.
  13. Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solids Struct., 48(18), 2496-2510. https://doi.org/10.1016/j.ijsolstr.2011.05.002.
  14. Hadjesfandiari, A.R., Hadjesfandiari, A., Zhang, H. and Dargush, G.F. (2018), "Size-dependent couple stress Timoshenko beam theory", preprint arXiv:1712.08527.
  15. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of the Laplace transform", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.
  16. Kang, X., Yang, FJ. and He, XY. (2012), "Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory", Acta Mechanica Sinica, 28(1), 104-111. https://doi.org/10.1007/s10409-012-0019-5.
  17. Kaushal, S., Kumar, R. and Miglani, A. (2010), "Response of frequency domain in generalized thermoelasticity with two temperatures", J. Eng. Phys. Thermophys., 83(5), 1080-1088. https://doi.org/10.1007/s10891-010-0433-0.
  18. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", Int. J. Eng. Sci., 50(1), 256-267. https://doi.org/10.1016/j.ijengsci.2010.12.008.
  19. Koiter, W.T. (1964), "Couple stresses in the theory of elasticity, I and II", Nederl. Akad.Wetensch. Proc. Serial B, 67, 17-29.
  20. Kumar, R. and Devi, S. (2015), "Interaction due to Hall current and rotation in a modified couple stress elastic half-Space due to ramp-type loading", Comput. Meth. Sci. Technol., 21(4), 229-240. https://doi.org/10.12921/cmst.2015.21.04.007.
  21. Kumar, R., Devi, S. and Sharma, V. (2017), "Deformation due to expanding ring load in modified couple stress thermoelastic diffusion in time and frequency domain", Mech. Adv. Mater. Struct., 24(8), 685-697. https://doi.org/10.1080/15376494.2016.1196775.
  22. Kumar, R., Sharma, N. and Lata, P. (2016), "Effects of Hall current and two temperatures in transversely isotropic magnetothermoelastic with and without energy dissipation due to ramp type heat", Mech. Adv. Mater. Struct., 24(8), 625-635. https://doi.org/10.1080/15376494.2016.1196769.
  23. Kumar, R., Sharma, N. and Lata, P. (2016a), "Thermomechanical interactions due to Hall current in transversely isotropic thermoelastic medium with and without energy dissipation with two temperatures and rotation", J. Solid Mech., 8(4), 840-858.
  24. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S. M. (2017a), "Mathematical modelling of Stoneley wave in a transversely isotropic thermoelastic media", Appl. Appl. Math., 12(1), 319-336.
  25. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017), "Rayleigh waves in anisotropic magnetothermoelastic medium", Coupled Syst. Mech., 6(3), 317-333. https://doi.org/10.12989/csm.2017.6.3.317.
  26. Lata, P. and Kaur, I. (2019), "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.
  27. Lata, P. and Kaur, I. (2019a), "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.2019.69.6.60.
  28. Lata, P. and Kaur, I. (2019a), "Thermomechanical interactions in a transversely isotropic magnato thermoelastic solids with two temperature and rotation due to time harmonic sources", Coupled Syst. Mech., 8(3), 219-245. http://doi.org/10.12989/csm.2019.8.3.219.
  29. Li, Y., Meguid, S.A., Fu, Y. and Xu, D. (2013), "Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam", Proc. Royal Soc. A Math. Phys. Eng. Sci., 470(2162), 1-17. https://doi.org/10.1098/rspa.2013.0473.
  30. Marin, M. (2007), "Weak solutions in elasticity of dipolar porous materials", Math. Prob. Eng., 2008, 1-8. http://dx.doi.org/10.1155/2008/158908.
  31. Marin, M. (1997), "On weak solutions in elasticity of dipolar bodies with voids", J. Comput. Appl. Math., 82(1-2), 291-297. https://doi.org/10.1016/S0377-0427(97)00047-2.
  32. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas (Havana), 16(2), 101-109.
  33. Marin, M. and Stan, G. (2013), "Weak solutions in elasticity of dipolar bodies with stretch", Carpathian J. Math., 29(1), 33-40. http://dx.doi.org/10.1155/2008/158908.
  34. Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of couple-stress in linear elasticity", Arch. Rational Mech. Anal., 11(1), 415-448. https://doi.org/10.1007/BF00253946.
  35. Najafi, M., Rezazadeh, G. and Shabani, R. (2012), "Thermoelastic damping in a capacitive micro-beam resonator considering hyperbolic heat conduction model and modified couple stress theory", J. Solid Mech., 4(4), 386-401.
  36. Othman M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a nonhomogeneous isotropic hollow cylinder with energy dissipation", Int. J. Thermophys., 33(5), 913-923. https://doi.org/10.1007/s10598-011-9102-1.
  37. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2013), "Generalized magneto-thermo-microstretch elastic solid under gravitational effect with energy dissipation" Multidiscipline Model. Mater. Struct., 9(2), 145-176. https://doi.org/10.1108/MMMS-01-2013-0005.
  38. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2015), "The effect of gravity on plane waves in a rotating thermomicrostretch elastic solid for a mode-I crack with energy dissipation" Mech. Adv. Mater. Struct., 22(11), 945-955. https://doi.org/10.1080/15376494.2014.884657.
  39. Othman, M.I.A., Jahangir, A. and Nadia, A. (2018a), "Microstretch thermoelastic solid with temperature-dependent elastic properties under the influence of magnetic and gravitational field", J. Brazilian Soc. Mech. Sci. Eng., 40(7), 332. https://doi.org/10.1007/s40430-018-1204-7.
  40. Press, W.H., Teukolsky, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipe, Cambridge University Press.
  41. Roque, C.M.C., Ferreira, A.J.M. and Reddy, J.N. (2013), "Analysis of Mindlin micro plates with a modified couple stress theory and a meshless method", Appl. Math. Modell., 37(7), 4626-4633. https://doi.org/10.1016/j.apm.2012.09.063.
  42. Shaat, M., Mahmoud, F.F., Gao, X.L. and Faheem, A.F. (2014), "Size dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects", Int. J. Mech. Sci., 79, 31-37. https://doi.org/10.1016/j.ijmecsci.2013.11.022.
  43. 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.
  44. Slaughter, W.S. (2002), The Linearised Theory of Elasticity, Birkhauser Boston, Cambridge, Massachusetts, U.S.A.
  45. Thai, H.T., Vo, T.P., Nguyen, T.K. and Lee, J. (2014), "Sizedependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory", Compos. Struct., 123, 337-349. https://doi.org/10.1016/j.compstruct.2014.11.065.
  46. Tiwari, G. (1971), "Effect of couple-stresses in a semi-infinite elastic medium due to impulsive twist over the surface", Pure Appl. Geophys., 91(1), 71-75. https://doi.org/10.1007/BF00877889.
  47. Togun, N. and Bagdatli, S.M. (2017), "Investigation of the size effect in Euler-Bernoulli nanobeam using the modified couple stress theory", Celal Bayar Univ. J. Sci., 13(4), 893-899. https://doi.org/10.18466/cbayarfbe.370362.
  48. Usman, M., Saba, K., Jahangir, A., Kamran, M. and Muhammad, N. (2018b), "Electromechanical fields and their influence on the internal quantum efficiency of GaN-based light-emitting diodes", Acta Mechanica Solida Sinica, 31(3), 383-390. https://doi.org/10.1007/s10338-018-0013-y.
  49. Wang, L., Xu, Y. and Ni, Q. (2013), "Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: A unified treatment", Int. J. Eng. Sci., 68, 1-10. https://doi.org/10.1016/j.ijengsci.2013.03.004.
  50. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  51. Zenkour, A.M. (2018), "Modified couple stress theory for micromachined beam resonators with linearly varying thickness and various boundary conditions", Arch. Mech. Eng., 65(1), 41-64. https://doi.org/10.24425/119409.
  52. Zenkour, A.M. and Abbas, I.A. (2014b), "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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