Coupled systems mechanics

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Time Harmonic interactions in the axisymmetric behaviour of transversely isotropic thermoelastic solid using New M-CST

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Harpreet (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2020.03.22
  • Accepted : 2020.10.19
  • Published : 2020.12.25
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Abstract

The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solid with new modified couple stress theory without energy dissipation and with two temperatures in frequency domain. The time harmonic sources and Hankel transform technique have been employed to find the general solution to the field equations.Concentrated normal force, normal force over the circular region, thermal point source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of angular frequency on the resulted quantities.

Keywords

References

  1. Abbas, I.A. (2014), "Three-phase lag model on thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity", J. Comput. Theo. Nanosci., 11(4), 987-992. https://doi.org/10.1166/jctn.2014.3454.
  2. Abbas, I.A. (2016), "Free vibration of a thermoelastic hollow cylinder under two-temperature generalized thermoelastic theory", Mech. Bas. Des. Struct. Mach., 45(3), 395-405. https://doi.org/10.1080/15397734.2016.1231065.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic microcomposite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  4. Arani Ghorbanpour, A., Abdollahian, M. and Jalaei, H.M. (2015), "Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory", J. Theo. Biology, 367, 29-38. https://doi.org/10.1016/j.jtbi.2014.11.019.
  5. 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.
  6. Atanasov, M.S., Karlicic, D., Kozic, P. and Janevski, G. (2017), "Thermal effect on free vibration and buckling of a double-microbeam system", Facta Universitatis, Series: Mech. Eng., 15(1), 45-62. https://doi.org/10.22190/FUME161115007S.
  7. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "Asimple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  8. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  9. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  10. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. http://dx.doi.org/10.12989/anr.2019.7.3.191.
  11. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  12. 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. https://doi.org/10.1007/s00419-013-0802-1.
  13. Chen, W., Li, L. and Xu, M. (2011), "A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation", Compos. Struct., 93, 2723-2732. https://doi.org/10.1016/j.compstruct.2011.05.032.
  14. Cosserat, E. and Cosserat, F. (1909), Theory of Deformable Bodies, Hermann et Fils, Paris, France.
  15. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi A. and Mahmoud S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  16. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017), "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.
  17. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Two-temperature theory in magnetothermoelasticity with fractional order dual-phase-lag heat transfer", Nucl. Eng. Des., 252, 267-277. https://doi.org/10.1016/j.nucengdes.2012.06.012.
  18. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/gae.2017.13.3.385.
  19. Fakhrabadi, S.M.M. (2017), "Application of modified couple stress theory and homotopy perturbation method in investigation of electromechanical behaviours of carbon manotubes", Adv. Appl. Math. Mech., 9(1), 23-42. https://doi.org/10.4208/aamm.2014.m71.
  20. Fang, Y., Li, P. and Wang, Z. (2013), "Thermoelastic damping in the axisymmetric vibration of circular microplate resonators with two dimensional heat conduction", J. Therm. Stress., 36, 830-850. https://doi.org/10.1080/01495739.2013.788406.
  21. Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solid. Struct., 48(18), 2496-2510. https://doi.org/10.1016/j.ijsolstr.2011.05.002.
  22. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  23. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  24. Kaur, H. and Lata, P. (2020a), "Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures", Steel Compos. Struct., 34(2), 309-319. https://doi.org/10.12989/scs.2020.34.2.309.
  25. 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.
  26. Ke, L.L. and Wang, Y. S. (2011), "Size effect on dynamic stability of functionally graded micro beams based on a modified couple stress theory", Compos. Struct., 93, 342-350. https://doi.org/10.1016/j.compstruct.2010.09.008.
  27. Koiter, W.T. (1964), "Couple-stresses in the theory of elasticity", Proc. Nat. Acad. Sci., 67, 17-44.
  28. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2008), "The size-dependent natural frequency of Bernoulli-Euler micro-beam", Int. J. Eng. Sci., 46, 427-437. https://doi.org/10.1016/j.ijengsci.2007.10.002.
  29. Kumar, R. and Devi, S. (2016), "A problem of thick circular plate in modified couple stress theory of thermoelastic diffusion", Cogent Math., 3(1), 1-14. http://dx.doi.org/10.1080/23311835.2016.1217969.
  30. Kumar, R., Sharma, N. and Lata, P. (2016b), "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.
  31. 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.
  32. Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. http://doi.org/10.12989/scs.2018.27.4.439.
  33. Lata, P. and Kaur, H. (2019a), "Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain", Geomech. Eng., 19(5), 369-381. https://doi.org/10.12989/gae.2019.19.5.369.
  34. Lata, P. and Kaur, H. (2019), "Axisymmetric deformation in transversely isotropic thermoelastic medium using new modified couple stress theory", Coupl. Syst. Mech., 8(6), 501-522. https://doi.org/10.12989/csm.2019.8.6.501.
  35. Lata, P. and Kaur, H. (2020), "Effect of two temperature on isotropic modified couple stress thermoelastic medium with and without energy dissipation", Geomech. Eng., 21(5), 461-469. https://doi.org/10.12989/gae.2020.21.5.461.
  36. Ma, H.M., Gao, X.L. and Reddy, J.N. (2008), "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solid., 56, 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007.
  37. Ma, H.M., Gao, X.L. and Reddy, J.N. (2011), "A non-classical Mindlin plate model based on a modified couple stress theory", Acta Mechanica, 220(1-4), 217-235. http://doi.org/10.1007/s00707-011-0480-4.
  38. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas (Havana), 16(2), 101-109.
  39. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlin. Anal.: Real World Appl., 10, 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001.
  40. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpath. J. Math., 33(2), 219-232. https://doi.org/10.37193/CJM.2017.02.09
  41. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  42. Mehralian, F. and TadiBeni, Y. (2017), "Thermo-electromechanical buckling analysis of cylindrical nanoshell on the basis of modified couple stress theory", J. Mech. Sci. Technol., 31(4), 1773-1787. https://doi.org/10.1007/s12206-017-0325-8.
  43. Othman, M.I.A. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory", Result. Phys., 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.012.
  44. 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/s10765-012-1202-4.
  45. 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", Multidisc. Model. Mater. Struct., 9(2), 145-176. https://doi.org/10.1108/MMMS-01-2013-0005.
  46. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2015), "The effect of gravity on plane waves in a rotating thermo-microstretch 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.
  47. Park, S.K. and Gao, X.L. (2006), "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng., 16, 2355. https://doi.org/10.1088/0960-1317/16/11/015.
  48. Park, S.K. and Gao, X.L. (2008), "Variational formulation of a modified couple stress theory and its application to a simple shear problem", Zeitschrift fürAngewandte Mathematik und Physik, 59, 904-917. https://doi.org/10.1007/s00033-006-6073-8
  49. Press, W.H., Teukolsky, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipe, Cambridge University Press.
  50. Rafiq, M., Singh, B., Arifa, S., Nazeer, M., Usman, M., Arif, S., Bibi, M. and Jahangir, A. (2019), "Harmonic waves solution in dual-phase-lag magneto-thermoelasticity", Open Phys., 17(1), 8-15. https://doi.org/10.1515/phys-2019-0002.
  51. 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.
  52. Simsek, M., Kocaturk, T. and Akbas, S.D. (2013), "Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory", Compos. Struct., 95, 740-747. http://doi.org/10.1016/j.compstruct.2012.08.036.
  53. Slaughter, W.S (2002), The Linearised theory of Elasticity, Birkhausar.
  54. Sobhy, M. and Radwan, A.F. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(1), 1750008-29. https://doi.org/10.1142/S1758825117500089.
  55. Tsiatas, G.C. (2009), "A new Kirchhoff plate model based on a modified couple stress theory", Int. J. Solid. Struct., 46, 2757-2764. https://doi.org/10.1016/j.ijsolstr.2009.03.004.
  56. Tsiatas, G.C. and Katsikadelis, J.T. (2009), "A BEM solution to the Saint-Venant torsion problem of microbar", Advances in Boundary Element TechniquesX, Eds. Sapountzakis, E.J. and Aliabadi, M.H., EC Ltd Publications, Eastleigh, UK, July.
  57. Yin, L, Qian, Q., Wang, L. and Xia, W. (2010), "Vibration analysis of microscale plates based on modified couple stress theory", Acta Mechanica Solida Sinica, 23(5), 386-393. http://dx.doi.org/101016/S0894-9166(10)60040-7. https://doi.org/10.1016/S0894-9166(10)60040-7
  58. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.

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