Advances in materials Research

  • 제13권5호
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  • Pages.417-429
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  • 2024
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  • 2234-0912(pISSN)
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  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
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Time harmonic interactions in a nonlocal isotropic thermoelastic thick circular plate without energy dissipation

  • Sukhveer Singh (Punjabi University APS Neighbourhood Campus) ;
  • Parveen Lata (Department of Mathematics, Punjabi University Patiala)
  • 투고 : 2022.01.17
  • 심사 : 2024.09.04
  • 발행 : 2024.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The research paper is devoted to study of the thermomechanical deformations occurring in a nonlocal homogeneous isotropic thick circular plate with frequency domain and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free subjected to axisymmetric heatsupply. Hankel transform has been used to find the analytical solutions. The expressions for physical quantities such as displacement components, stress components and conductive temperature have been obtained in the transformed domain. The resulting quantities in the physical domain have been obtained by using the numerical inversion technique. The numerical simulated results have been depicted graphically to study the effect of nonlocality and two temperature on the components of displacement, stress components and conductive temperature.

키워드

참고문헌

  1. Abbas, I.A. (2014a), "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. (2014b), "Fractional order GN model on thermoelastic interaction in an infinite fibre-reinforced anisotropic plate containing a circular hole", J. Comput. Theoret. Nanosci., 11(2), 380-384. https://doi.org/10.1166/jctn.2014.3363. 
  3. Abbas, I.A., Abdalla, A.E.N.N., Alzahrani, F.S. and Spagnuolo, M. (2016), "Wave propagation in a generalized thermoelastic plate using eigenvalue approach", J. Therm. Stress., 39(11), 1367-1377. https://doi.org/10.1080/01495739.2016.1218229. 
  4. Abbas, I.A., Marin, M., Abouelmagd, E.I. and Kumar, R. (2015), "A green and naghdi model in a two-dimensional thermoelastic diffusion problem for a half space", J. Comput. Theoret. Nanosci., 12(2), 280-286. https://doi.org/10.1166/jctn.2015.3729. 
  5. Abo-Dahab, S.M. and Abbas, I.A. (2011), "LS model on thermal shock problem of generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity", Appl. Math. Model., 35(8), 3759-3768. https://doi.org/10.1016/j.apm.2011.02.028. 
  6. Abouelregal, A.E. and Zenkour, A.M. (2017), "Two-temperature thermoelastic surface waves in micropolar thermoelastic media via dual-phase-lag model", Adv. Aircr. Spacecr. Sci., 4(6), 711-727. https://doi.org/10.12989/aas.2017.4.6.711. 
  7. Abouelregal, A.E., Askar, S.S., Marin, M. and Mohamed, B. (2023), "The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod", Sci. Rep., 13, 9052. https://doi.org/10.1038/s41598-023-36371-2. 
  8. 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. Aircr. Spacecr. Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001. 
  9. 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. 
  10. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys., 19(4), 614-627. https://doi.org/10.1007/BF01594969. 
  11. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", J. Appl. Math. Phys., 20(1), 107-112. https://doi.org/10.1007/BF01591120. 
  12. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publisher Corporation, New Delhi, India. 
  13. Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Ration. Mech. Anal., 43(1), 24-35.  https://doi.org/10.1007/BF00251543
  14. Edelen, D.G.B., Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Ration. Mech. Anal., 43(1), 36-44.  https://doi.org/10.1007/BF00251544
  15. El-Nabulsi, R.A. (2018), "Nonlocal approach to nonequilibrium thermodynamics and nonlocal heat diffusion processes", Contin. Mech. Thermodyn., 30(4), 889-915. https://doi.org/10.1007/s00161-018-0666-2. 
  16. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0. 
  17. Eringen, A.C.A. and Wegner, J.L.R. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56(2), B20-B22. https://doi.org/10.1115/1.1553434. 
  18. Fabrizio, M., Lazzari, B. and Nibbi, R. (2011), "Thermodynamics of non-local materials: extra fluxes and internal powers", Contin. Mech. Thermodyn., 23(6), 509. https://doi.org/10.1007/s00161-011-0193-x. 
  19. Gao, Y., Xiao, W. shen and Zhu, H. (2019), "Nonlinear vibration of different types of functionally graded nanotubes using nonlocal strain gradient theory", Eur. Phys. J. Plus, 134(7), 205-219. https://doi.org/10.1140/epjp/i2019-12735-6. 
  20. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136. 
  21. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-208. https://doi.org/10.1007/BF00044969. 
  22. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X. 
  23. Hosseini, S.M. (2020), "A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with energy dissipation", Struct. Eng. Mech., 73(3), 287-302. https://doi.org/10.12989/sem.2020.73.3.287. 
  24. Hu, W., Deng, Z., Han, S. and Zhang, W. (2013), "Generalized multi-symplectic integrators for a class of Hamiltonian nonlinear wave PDEs", J. Comput. Phys., 235, 394-406. https://doi.org/10.1016/j.jcp.2012.10.032. 
  25. Hu, W., Han, Z., Bridges, T. J. and Qiao, Z. (2023a), "Multi-symplectic simulations of W/M-shape-peaks solitons and cuspons for FORQ equation", Appl. Math. Lett., 145, 108772. https://doi.org/10.1016/j.aml.2023.108772. 
  26. Hu, W., Huai, Y., Xu, M., Feng, X., Jiang, R., Zheng, Y. and Deng, Z. (2021b), "Mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids", Mech. Syst. Signal Pr., 159, 107833. https://doi.org/10.1016/j.ymssp.2021.107833. 
  27. Hu, W., Xi, X., Song, Z., Zhang, C. and Deng, Z.(2023b), "Coupling dynamic behaviors of axially moving cracked cantilevered beam subjected to transverse harmonic load", Mech. Syst. Signal Pr., 204, 110757. https://doi.org/10.1016/j.ymssp.2023.110757. 
  28. Hu, W., Xu, M., Song, J., Gao, Q. and Deng, Z. (2021a), "Coupling dynamic behaviors of flexible stretching hub-beam system", Mech. Syst. Signal Pr., 151, 107389. https://doi.org/10.1016/j.ymssp.2020.107389.
  29. Hu, W., Xu, M., Zhang, F., Xiao, C. and Deng, Z. (2022), "Dynamic analysis on flexible hub-beam with step-variable cross-section", Mech. Syst. Signal Pr., 180, 109423. https://doi.org/10.1016/j.ymssp.2022.109423. 
  30. Hu, W., Ye, J. and Deng, Z. (2020), "Internal resonance of a flexible beam in a spatial tethered system", J. Sound Vib., 475, 115286. https://doi.org/10.1016/j.jsv.2020.115286. 
  31. Hu, W., Zhang, C. and Deng, Z. (2020), "Vibration and elastic wave propagation in spatial flexible damping panel attached to four special springs", Commun. Nonlinear Sci. Numer. Simul., 84, 105199. https://doi.org/10.1016/j.cnsns.2020.105199. 
  32. Huai, Y., Hu, W., Song, W., Zheng, Y and Deng, Z. (2023), "Magnetic-field-responsive property of Fe3O4/polyaniline solvent-free nanofluid", Phys. Fluid, 35(1), 012001. https://doi.org/10.1063/5.0130588. 
  33. Hussain, M., Naeem, M.N. and Tounsi, A. (2020), "Numerical study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Constr., 9(3), 301-312. https://doi.org/10.12989/acc.2020.9.3.301. 
  34. Kumar, R., Marin, M. and Abbas, I.A. (2015), "Axisymmetric distributions of thick circular plate in a modified couple stress theory", J. Molecul. Eng. Mater., 3, 1550004. https://doi.org/10.1142/S2251237315500045. 
  35. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33(1), 955-963. https://doi.org/10.12989/scs.2019.33.1.123. 
  36. Lata, P. and Singh, S. (2020), "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. 
  37. Lata, P. and Singh, S. (2021a), "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. 
  38. Lata, P. and Singh, S. (2021b), "Effects due to two temperature and hall current in a nonlocal isotropic magneto-thermoelastic solid with memory dependent derivatives", Coupled Syst. Mech., 10(4) 351-369. https://doi.org/10.12989/csm.2021.10.4.351. 
  39. Lata, P. and Singh, S. (2022), "Axisymmetric deformations in a nonlocal isotropic thermoelastic solid with two temperature", Forces Mech., 6, 100068. https://doi.org/10.1016/j.finmec.2021.100068. 
  40. Liani, M., Moulay, N., Bourada, F., Addou, F.Y., Bourada, M., Tounsi, A. and Hussain, M. (2022), "A nonlocal integral Timoshenko beam model for free vibration analysis of SWCNTs under thermal environment", Adv. Mater. Res., 11(1), 1-22. https://doi.org/10.12989/amr.2022.11.1.001. 
  41. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Rev. Acad. Canar., 8(1), 101-106 
  42. Marin, M. (1997), "On the domain of analyticity", Arch. Math., 33(1), 301-308. 
  43. Mohamed, R.A., Abbas, I.A. and Abo-Dahab, S.M. (2009), "Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction", Commun. Nonlinear Sci. Numer. Simul., 14(4), 1385-1395. https://doi.org/10.1016/j.cnsns.2008.04.006. 
  44. Othman, M.I.A., Said, S. and Marin, M. (2019), "A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model", Int. J. Numer. Method. Heat Fluid Flow, 29(12), 4788-4806. https://doi.org/10.1108/HFF-04-2019-0359. 
  45. Press, W.H., Teukolshy, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge, UK. 
  46. Saeed, T., Abbas, I. and Marin, M. (2020), "A GL model on thermo-elastic interaction in a poroelastic material using finite element method", Symmetry, 12(3), 1-24. https://doi.org/10.3390/sym12030488. 
  47. Sellitto, A. and Di Domenico, M. (2019), "Nonlocal and nonlinear contributions to the thermal and elastic high-frequency wave propagations at nanoscale", Contin. Mech. Thermodyn., 31(3), 807-821. https://doi.org/10.1007/s00161-018-0738-3. 
  48. Singh, S. and Lata, P. (2023), "Effect of two temperature and nonlocality in an isotropic thermoelastic thick circular plate without energy dissipation", Partial Differ. Equ. Appl. Math., 7, 100512. https://doi.org/10.1016/j.padiff.2023.100512. 
  49. Yadav, A.K., Carrera, E., Marin, M. and Othman, M.I.A. (2024), "Reflection of hygrothermal waves in a Nonlocal Theory of coupled thermo-elasticity", Mech. Adv. Mater. Struct., 31(5), 1083-1096. https://doi.org/10.1080/15376494.2022.2130484. 
  50. Youssef, H.M. (2006), "Theory of two-temperature-generalized thermoelasticity", IMA Journal of Applied Mathematics, 71(3), 383-390.  https://doi.org/10.1093/imamat/hxh101
  51. Youssef, H.M. and Al-Lehaibi, E.A. (2007), "State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem", Int. J. Solids Struct., 44(5), 1550-1562. https://doi.org/10.1016/j.ijsolstr.2006.06.035. 
  52. Zenkour, A.M. and Abbas, I.A. (2013), "Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method", J. Vib. Control, 20(12), 1907-1919. https://doi.org/10.1177/1077546313480541. 
  53. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. https://doi.org/10.12989/cac.2020.26.1.063.