Advances in nano research

  • 제16권2호
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  • Pages.141-154
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  • 2024
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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Thermoelastic deformation properties of non-localized and axially moving viscoelastic Zener nanobeams

  • Ahmed E. Abouelregal (Department of Mathematics, College of Science and Arts, Jouf University) ;
  • Badahi Ould Mohamed (Faculty of Sciences and Technology, University of Nouakchott) ;
  • Hamid M. Sedighi (Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz)
  • 투고 : 2023.07.19
  • 심사 : 2023.10.30
  • 발행 : 2024.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study aims to develop explicit models to investigate thermo-mechanical interactions in moving nanobeams. These models aim to capture the small-scale effects that arise in continuous mechanical systems. Assumptions are made based on the Euler-Bernoulli beam concept and the fractional Zener beam-matter model. The viscoelastic material law can be formulated using the fractional Caputo derivative. The non-local Eringen model and the two-phase delayed heat transfer theory are also taken into account. By comparing the numerical results to those obtained using conventional heat transfer models, it becomes evident that non-localization, fractional derivatives and dual-phase delays influence the magnitude of thermally induced physical fields. The results validate the significant role of the damping coefficient in the system's stability, which is further dependent on the values of relaxation stiffness and fractional order.

키워드

참고문헌

  1. Abouelregal, A.E., Marin, M. and Askar, S.S. (2023), "Analysis of the magneto-thermoelastic vibrations of rotating Euler- Bernoulli nanobeams using the nonlocal elasticity model", Bound. Value Probl., 21. https://doi.org/10.1186/s13661-023-01706-5 
  2. Abouelregal, A.E. and Marin, M. (2020), "The response of nanobeams with temperature-dependent properties using state-space method via modified couple stress theory", Symmetry, 12, 1276. https://doi.org/10.3390/sym12081276 
  3. Abouelregal, A.E. and Sedighi, H.M. (2022), "Thermoelastic characteristics of moving viscoelastic nanams based on the nonlocal couple stress theory and dual-phase lag model", Phys. Scr., 97(11), 3. https://doi.org/10.1088/1402-4896/ac97cc 
  4. Alazwari, M.A., Esen I, Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermomagnetic fields and moving load", Adv. Nano Res., 12(3), 231-51. https://doi.org/10.12989/anr.2022.12.3.231 
  5. Aliasghary, M., Mobki, H., Ouakad, H.M. (2022), "Pull-in phenomenon in the electrostatically micro-switch suspended between two conductive plates using the artificial neural network", J. Appl. Comput. Mech., 8(4), 1222-1235. https://doi.org/10.22055/jacm.2021.38569.3248 
  6. Anjum, N., He, J., He, C., Ashiq, A. (2022), "A brief review on the asymptotic methods for the periodic behaviour of microelectron-mechanical systems", J. Appl. Comput. Mech., 8(3), 1120-1140. https://doi.org/10.22055/jacm.2022.39404.3401 
  7. Arhami, M., Koochi, A. and Gharib, M.R. (2022), "Nonlocal coupled thermoelastic analysis of nanobeam under Casimir force", Arch. Appl. Mech., 92, 3729-3746. https://doi.org/10.1007/s00419-022-02258-3 
  8. Askarian, A.R., Permoon, M.R. and Shakouri, M. (2020), "Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions", Int. J. Mech. Sci., 179, 105702. https://doi.org/10.1016/j.ijmecsci.2020.105702 
  9. Atanackovic, T.M. and Pilipovic, S. (2022), "Zener model with general fractional calculus: thermodynamical restrictions", Fractals, 6, 617. https://doi.org/10.3390/fractalfract6100617 
  10. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037 
  11. Bagley, R.L. and Torvik, P.J. (1983), "Fractional calculus-a different approach to the analysis of viscoelastically damped structures", AIAA J., 21(5), 741-748. https://doi.org/10.2514/3.8142 
  12. Bagley, R.L. and Torvik, P.J. (1983), "A theoretical basis for the application of fractional calculus to viscoelasticity", J. Rheol., 27(3), 201-210. https://doi.org/10.1122/1.549724 
  13. E. Blanc, D. Komatitsch, E. Chaljub, B. Lombard, Z. Xie, (2016), "Highly-accurate stability preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of attenuation," Geophys. J. Int., 205, 427-439.  https://doi.org/10.1093/gji/ggw024
  14. Borjalilou, V. and Asghari, M.E. (2020), "Thermoelastic damping nonlocal nanobeams considering dual-phase-lagging effect", J. Vib. Control, 26(11-12), 1042-1053. https://doi.org/10.1177/1077546319891334 
  15. Caputo, M. and Mainardi, F. (1971), "A new dissipation model based on memory mechanism", Pure Appl. Geophys., 91, 147. https://doi.org/10.1007/BF00879562 
  16. Cattaneo, C. (2011), Sulla Conduzione Del Calore, Springer, Berlin Heidelberg. 
  17. Chen, L.Q. (2005), "Analysis and control of transverse vibrations of axially moving strings", Appl. Mech. Rev., 58(2), 91. https://doi.org/10.1115/1.1849169 
  18. Das, S. (2011), Functional fractional calculus, Springer, Berlinm Hidelberg. 
  19. Di Pa, M., Pirrotta, A., and Valenza, A. (2011), "Visco-elastic behavior through fractional calculus: easier method for best fitting experimental results," Mech. Mat., 43, 799-806. https://doi.org/10.1016/j.mechmat.2011.08.016 
  20. Duwel, A., Gorman, J., Weinstein, M., Borenstein, J. and Ward, P. (2003), "Experimental study of thermoelastic damping in MEMS gyros", Sensors Actuat. A, 20, 70-75. https://doi.org/10.1016/S0924-4247(02)00318-7 
  21. Ece, A.E., Marin, M. and Askar, S.S. (2023), "Generalized MGT heat transfer model for an electro-thermal microbeam lying on a viscous-Pasternak foundation with a laser excitation heat source", Symmetry, 15, 814. https://doi.org/10.3390/sym15040814 
  22. Ece, M.C. and Aydogdu, M. (2007), "Nonlocal elasticity effect on vibration in-plane loaded double-walled carbon nano-tubes", Acta Mech., 190(1-4), 185-195. https://doi.org/10.1007/s00707-006-0417-5 
  23. Eldred, L.B., Baker, W.P. and Palazotto, A.N. (2005), "Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials", AIAA J., 33, 547. https://doi.org/10.2514/3.12471 
  24. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5 
  25. Eringen, A.C. (1972), "Linear theory nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10, 425-435. https://doi.org/10.1016/0020-7225(72)90050-X 
  26. Eringen, A.C. (1983), "On differential Eqs. of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803 
  27. Eringen, A.C. (2002), "Nonlocal Continuum Field Theories", Springer, New York, NY, USA. 
  28. Farno, E., Baudez, J.C. and Eshtiaghi, N. (2018), "Comparison between classical Kelvin-Voigt and fractional derivative Kelvin-Voigt models in prediction of linear viscoelastic behaviour of waste activated sludge", Sci. Total Environ., 613-614, 1031-1036. https://doi.org/10.1016/j.scitotenv.2017.09.206 
  29. Faghidian SA, Tounsi A. (2022), "Dynamic characteristics of mixture unified gradient elastic nanobeams", Facta Universitatis, Series: Mechanical Engineering, 20(3), 539-52.  https://doi.org/10.22190/FUME220703035F
  30. Farno, E., Baudez, J.C., Parthasarathy, R. and Eshtiaghi, N. (2014), "Rheological characterisation of thermally-treated anaerobic digested sludge: impact of temperature and thermal history", Water Res., 56, 161. https://doi.org/10.1016/j.watres.2014.02.048 
  31. Jalil, A. T., Saleh, Z. M., Imran, A. F., Yasin, Y., Ruhaima, A. A. K., Gatea, M. A., and Esmaeili, S. (2023). A size-dependent generalized thermoelasticity theory for thermoelastic damping in vibrations of nanobeam resonators. Int. J. Struct. Stab. Dyn., 23(12), 2350133. 
  32. Green, A.E., and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stresses, 15, 253-264. https://doi.org/10.1080/01495739208946136 
  33. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elasticity, 31, 189-208. https://doi.org/10.1007/BF00044969 
  34. Grover, D., and Seth, R.K. (2018), "Viscothermoelastic microscale beam resonators based on dual-phase lagging model", Microsyst. Technol., 24, 1667-1672.  https://doi.org/10.1007/s00542-017-3515-5
  35. Hamidi, B.A., Hosseini, S.A., Hassannejad, R., and Khosravi, F. (2020), "Theoretical analysis of thermoelastic damping of silver nanobeam resonators based on Green-Naghdi via nonlocal elasticity with surface energy effects", Eur. Phys. J. Plus, 135, 1-20.  https://doi.org/10.1140/epjp/s13360-019-00059-2
  36. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of the Laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X 
  37. Huang, Y., Fu, J. and Liu, A. (2019), "Dynamic instability of Euler-Bernoulli nanobeams subject to parametric excitation", Compos. B, 164, 234. https://doi.org/10.1016/j.compositesb.2018.11.088 
  38. Jones, D. (2001), Handbook of Viscoelastic Vibration Damping, John Wiley and Sons. 
  39. Kulkarni, R.G. (2008), "Solving sextic equations," Atlantic Electr. J. Math., 3(1), 56-60. 
  40. Koutsoumaris, C.C. and Eptaimeros, K.G. (2021), "Nonlocal integral static problems of nanobeams resting on elastic foundation", Eur. J. Mech. A Solids, 89, 104295. https://doi.org/10.1016/j.euromechsol.2021.104295 
  41. Kumar, R., Kaushal, S. and Vikram, D. (2022), "Dynamic mathematical model of modified couple stressermoelastic diffusion with phase-lag", Int. Appl. Mech., 58, 348. https://doi.org/10.1007/s10778-022-01160-3 
  42. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids., 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X 
  43. Lewandowski, R., Slowik, M. and Przychodzki, M. (2017), "Parameters identification of fractional models of viscoelastic dampers and fluids", Struct. Eng. Mech., 63(2), 181-193. https://doi.org/10.12989/sem.2017.63.2.181 
  44. Li, C., Yao, L. and Chen, W.S. (2015), "Comments on nonlocal effects in nano-cantver beams", Int. J. Eng. Sci., 87, 47-57. https://doi.org/10.1016/j.ijengsci.2014.11.006 
  45. Lim, C.W., Li, C. and Yu, J.L. (2010), "Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach", Acta Mech. Sinica, 26(5), 755-765. https://doi.org/10.1007/s10409-010-0374-z 
  46. Liu, N., Yang, G. and Chen, B. (2014), "Transverse vibration analysis of an axially moving beam with lumped mass", J. Vibroeng., 16(7), 3209-3217. 
  47. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5 
  48. Mainardi, F. and Sp, G. (2011), "Creep, relaxation and viscosity properties for basic fractional models in rheology", Eur. Phys. J. Spec. Top., 193, 133-160. https://doi.org/10.1140/epjst/e2011-01387-1 
  49. Mead, D. (1999), Passive Vibration Control, John Wiley and Sons Inc. 
  50. Mindlin, R.D. and Eshel, N.N. (1968), "On first strain-gradient theories in linear elasticity", Int. J. Solids Struct., 4(1), 109-124. https://doi.org/10.1016/0020-7683(68)90036-X 
  51. Oparnica, L., and Suli, E. (2020), "Well-posedness of the fractional zener wave equation for heterogeneous viscoelastic materials", Fract. Calculus Appl. Anal., 23(1), 126-166. https://doi.org/10.1515/fca-2020-0005 
  52. Pham, Q.H., Nguyen, P.C., Tran, V.K., Lieu, Q.X. and Tran, T.T. (2023), "Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates", Eng. Comput., 39, 993-1018. https://doi.org/10.1007/s00366-022-01726-2 
  53. Podlubny, I. (1999), Fractional Differential Equations, Academic Press, San Diego. 
  54. Rahimi, Z., Sumelka, W. and Yang, X.J. (2017), "Linear and nonlinear free vibration of nano beams based on a new fractional non-local theory", Eng. Comput, 34(5), 1754-1770. https://doi.org/10.1108/EC-07-2016-0262 
  55. Roy Choudhuri, S.K. (2007), "On a thermoelastic three-phase-lag model", J. Therm. Stresses, 30, 231-238. https://doi.org/10.1080/01495730601130919 
  56. Shan, X. and Huang, A. (2022), "Intelligent simulation of the thermal buckling characteristics of a tapered functionally graded porosity-dependent rectangular small-scale beam", Adv. Nano Res., 12(3), 281-90. https://doi.org/10.12989/anr.2022.12.3.281 
  57. Sumelka, W., Blaszszyk, T. and Liebold, C. (2015), "Fractional Euler-Bernoulli beams: theory, numerical study and experimental validation", Eur. J. Mech. A Solids, 54, 243-251. https://doi.org/10.1016/j.euromechsol.2015.07.002 
  58. Thai, C.H., Nguyen-Xuan, H. and Phung-Van, P. (2022), "A size-dependent isogeometric analysis of laminated composite plates based on the nonlocal strain gradient theory," Eng. Comp., 39, 331-345.  https://doi.org/10.1007/s00366-021-01559-5
  59. Toupin, R.A. (1964), "Theories of elasticity with couple-stress", Arch. Ration. Mech. Anal., 17(2), 85. https://doi.org/10.1007/BF00253050 
  60. Tung, D.X. (2021), "Wave propagation in nonlocal orthotropic micropolar elastic solids", Arch. Mech., 73(3), 237-251. https://doi.org/10.24423/aom.3764 
  61. Tzou, D.Y. (1995), "The generalized lagging response in small-scale and high-rate heating", Int. J. Heat Mass Transfer, 38(17), 3231-3240. https://doi.org/10.1016/0017-9310(95)00052-B 
  62. Tzou, D.Y. (2015), "A unified field approach for heat conduction from macro- to micro-scales", J. Heat Trans., 117, 8-16. https://doi.org/10.1115/1.2822329 
  63. Tzou, D.Y. (2014), Macro-to Microscale Heat Transfer: the Lagging Behavior, John Wiley & Sons, West Sussex.
  64. Vernotte, P. (1958), "Les paradoxes de la theorie continue de l'Eq. de la chaleur", Comput. Rendus, 246, 3154. https://doi.org/10.1016/j.ijengsci.2017.06.006 
  65. Vincent, J.F.V. (1990), Structural Biomaterials, Princeton University Press. 
  66. Vajjaramatti, A., Balavalad, K.B. and Ashokkumar M. (2020), "Design, simulation and analysis of nems based piezoresistive pressure sensor", Int. J. Eng. Res. Technol., 9(7), 808-811. https://doi.org/10.17577/IJERTV9IS070342 
  67. Wu, F. and She, G.L. (2023), "Wave propagation in double nanobeams in thermal environments using the Reddy's high-order shear deformation theory", Adv. Nano Res., 14(6), 495-506. https://doi.org/10.12989/anr.2023.14.6.495 
  68. Xia, Z.X., Zhang, G.Y., Cong, Y. and Gu, S.T. (2002), "A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates", J. Sound Vib., 529, 116889. https://doi.org/10.1016/j.jsv.2022.116889 
  69. Xiao, R., Yakacki, C.M., Guo, J., Frick, C.P. and Nguyen, T.D. (2016), "A predictive parameter for the shape memory behavior of thermoplastic polymers", J. Polym. Sci. B Polym. Phys., 54(14), 1405-1414. https://doi.org/10.1002/polb.23981 
  70. Xiao, R., Sun, H., Chen, W. (2016), "An equivalence between generalized Maxwell model and fractional Zener model", Mech. Mater., 100, 148-153. https://doi.org/10.1016/j.mechmat.2016.06.016 
  71. Yang, F., 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 
  72. W. Yang, S. Wang, W. Kang, T. Yu, and Y. Li, (2023), "A unified high-order model for size-dependent vibration of nanobeam based on nonlocal strain/stress gradient elasticity with surface effect," Int. J. Eng. Sci., 182, 103785 
  73. Zhang, Y., Sahmani, S., Yang, Z. and Safaei, B. (2022), "Nonlocal and couple stress tensors three-dimensional nonlinear dynamical stability behavior of microshells manufactured by smart materials", Acta Mech., 233, 5377-5401. https://doi.org/10.1007/s00707-022-03394-1 
  74. Zhao, D., Liu, J. and Wang, L. (2016), "Linear free vibration of a cantilever nanobeam with surface effects: Semi-analytical solutions", Int. J. Mech. Sci., 113, 184-195. https://doi.org/10.1016/j.ijmecsci.2016.05.001 
  75. Zhou, H. and Li, P. (2017), "Thermoelastic damping in micro- and nanobeam resonators with non-fourier heat conduction", IEEE Sens. J., 17, 6966-6977. https://doi.org/10.1016/j.ijmecsci.2019.105211