Coupled systems mechanics

  • 제10권4호
  • /
  • Pages.351-369
  • /
  • 2021
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effects due to two temperature and hall current in a nonlocal isotropic magneto-thermoelastic solid with memory dependent derivatives

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University Patiala) ;
  • Singh, Sukhveer (Punjabi University APS Neighbourhood Campus)
  • 투고 : 2021.05.29
  • 심사 : 2021.07.09
  • 발행 : 2021.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

The paper is devoted to the study of thermomechanical interactions in a homogeneous nonlocal magneto-thermoelastic rotatingmediumunderthe effect of hall current and two temperaturewith memory dependent derivatives. Atwo-dimensional model has been assumed. Laplace and Fourier transforms have been used to find the solution to the problemin transformed domain. The analytical expressions of components of displacement,stress and current density and conductive temperature are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain and the results are depicted graphically to show the effect of nonlocal parameter on the components of displacements, stresses, current density and conductive temperature. The effect of nonlocal parameter and hall current parameter has been represented graphically by taking different values.

키워드

참고문헌

  1. Abbas, I.A. (2014), "A GN model based upon two temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity", Appl. Math. Comput., 245, 108-115. https://doi.org/10.1016/j.amc.2014.07.059.
  2. Abbas, I.A., Abo-El-Nour, N. and Othman, M.I. (2011), "Generalized magneto-thermoelasticity in a fiber-reinforced anisotropic half-space", Int. J. Thermophys., 32(5), 1071-1085. https://doi.org/10.1007/s10765-011-0957-3.
  3. Abouelregal, A.E. (2019), "Rotating magneto-thermoelastic rod with finite length due to moving heat sources via Eringen's nonlocal model", J. Comput. Appl. Mech., 50(1), 118-126, https:/doi.org/10.22059/jcamech. 2019.275893.360.
  4. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  5. Alzahrani, F.S. and Abbas, I. A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., 22(2), 369-386. https://doi.org/10.12989/scs.2016.22.2.369.
  6. Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133.
  7. Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized thermomicrostretch elastic solid", Int. J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9.
  8. Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A., ... Mahmoud, S.R. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. https://doi.org/10.12989/cac.2021.27.1.073.
  9. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  10. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  11. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircraf. Spacecraft Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.
  12. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.
  13. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys. (ZAMP), 19, 614-627. https://doi.org/10.1007/BF01594969.
  14. Dhaliwal R.S. and Singh A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publisher Corporation, New Delhi, India.
  15. Edelen, D.G.B., Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Rat. Mech. Anal., 43, 36-44. https://doi.org/10.1007/BF00251543.
  16. Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Rat. Mech. Anal., 43, 24-35. https://doi.org/10.1007/BF00251543.
  17. Eringen, A.C. (2002), Nonlocal Continum Field Theories, Springer, New York, USA.
  18. Ezzat, M. and El-Barrry, A.A. (2017b), "Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. https://doi.org/10.12989/scs.2017.24.3.297.
  19. 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., 25(2), 177-186. https://doi.org/10.12989/scs.2017.25.2.177.
  20. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  21. Jahangir, A., Tanvir, F. and Zenkour, A. (2020), "Reflection of photothermoelastic waves in a semiconductor material with different relaxations", Ind. J. Phys., 95(1), 51-59. https://doi.org/10.1007/s12648-020-01690-x.
  22. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  23. Khan, A.A., Bukhari, S.R., Marin, M. and Ellahi, R. (2019), "Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index", Heat Transf. Res., 50(11), 1061-1080. https://doi.org/10.1615/HeatTransRes.2018028397.
  24. Kumar, R., Sharma, N. and Lata, P. (2017), "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.
  25. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33 (1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.
  26. Lata, P. and Singh, S. (2020a), "Deformation in a nonlocal magneto-thermoelastic solid with hall current due to normal force", Geomech. Eng., 22(2), 109-117. https://doi.org/10.12989/gae.2020.22.2.109.
  27. Lata, P. and Singh, S. (2020b), "Time harmonic interactions in non local thermoelastic solid with two temperatures", Struct. Eng. Mech., 74(3), 341-350. https://doi.org/10.12989/sem.2020.74.3.341.
  28. Lata, P. and Singh, S. (2020c), "Thermomechanical interactions in a nonlocal thermoelastic model with two temperature and memory dependent derivatives", Coupl. Syst. Mech., 9(5), 397-410. https://doi.org/10.12989/csm.2020.9.5.397
  29. Lata, P. and Singh, S. (2020d), "Effects of nonlocality and two temperature in a nonlocal thermoelastic solid due to ramp type heat source", Arab J. Basic Appl. Sci., 27(1), 358-364. https://doi.org/10.1080/25765299.2020.1825157
  30. Lata, P. and Singh, S. (2020e), "Plane wave propagation in a nonlocal magneto-thermoelastic solid with two temperature and Hall current", Wave. Rand. Complex Media, 1-27. https://doi.org/10.1080/17455030.2020.1838667
  31. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Steel Compos. Struct., 38(2), 141-150. https://doi.org/10.12989/scs.2021.38.2.141
  32. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Revista de la Academia Canaria de Ciencias, 8(1), 101-106.
  33. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", Aip Adv., 5(3), Art. No. 037113. https://doi.org/10.1063/1.4914912.
  34. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A, Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  35. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  36. Othman, M.I. and Abbas, I.A. (2011), "Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method", Meccanica, 46(2), 413-421. https://doi.org/10.1007/s11012-010-9322-z.
  37. 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, 913-923. https://doi.org/10.1007/s10765-012-1202-4.
  38. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., ... Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/CAC.2020.25.4.311
  39. Saeed, T., Abbas, I. and Marin, M. (2020), "A GL model on thermo-elastic interaction in a poroelastic material using finite element method", Symm. Basel, 12(3), 1-24, Art. No. 488. https://doi.org/10.3390/sym12030488.
  40. Sharma, N., Kumar, R. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipiation 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.
  41. Soleimani, A., Dastani, K., Hadi, A. and Naei, M.H. (2019), "Effect of out of plane defects on the postbuckling behaviour of graphene sheets based on nonlocal elasticity theory", Steel Compos. Struct., 30(6), 517-534. https://doi.org/10.12989/scs.2019.30.6.517.
  42. Tahir, S.I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  43. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation", Wave. Rand. Complex Media, 1-24. https://doi.org/ 10.1080/17455030.2021.1942310.
  44. Youssef, H.M. (2006), "Theory of two-temperature-generalized thermoelasticity", IMA J. Appl. Math., 71, 383-390. https://doi.org/10.1093/imamat/hxh101.
  45. Youssef, H.M. and Al-Lehaibi, E.A. (2007), "State space approach of two-temperature generalized thermoelasticity of one-dimensional problem", Int. J. Solid. Struct., 44, 1550-1562. https://doi.org/10.1016/j.ijsolstr.2006.06.035.
  46. Zenkour, A.M. (2020), "Magneto-thermal shock for a fiber-reinforced anisotropic half-space studied with a refined multi-dual-phase-lag model", J. Phys. Chem. Solid., 137, 109213. https://doi.org/10.1016/j.jpcs.2019.109213.
  47. Zhang, L., Bhatti, M.M., Marin, M. and Mekheimer, K.S. (2020), "Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles", Entropy, 22(10), Art. No.1070. https://doi.org/10.3390/e22101070.