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Magnetic field effect on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic foundation

  • Yapanmis, Burak E. (Aliaga Vocational and Training School, Ege University) ;
  • Togun, Necla (Department of Mechanical Engineering, Gaziantep University) ;
  • Bagdatli, Suleyman M. (Department of Mechanical Engineering, Manisa Celal Bayar University) ;
  • Akkoca, Sevki (Department of Mechanical Engineering, Manisa Celal Bayar University)
  • Received : 2021.01.28
  • Accepted : 2021.07.23
  • Published : 2021.09.25

Abstract

The history of modern humanity is developing towards making the technological equipment used as small as possible to facilitate human life. From this perspective, it is expected that electromechanical systems should be reduced to a size suitable for the requirements of the era. Therefore, dimensionless motion analysis of beams on the devices such as electronics, optics, etc., is of great significance. In this study, the linear and nonlinear vibration of nanobeams, which are frequently used in nanostructures, are focused on. Scenarios have been created about the vibration of nanobeams on the magnetic field and elastic foundation. In addition to these, the boundary conditions (BC) of nanobeams having clamped-clamped and simple-simple support situations are investigated. Nonlinear and linear natural frequencies of nanobeams are found, and the results are presented in tables and graphs. When the results are examined, decreases the vibration amplitudes with the increase of magnetic field and the elastic foundation coefficient. Higher frequency values and correction terms were obtained in clamped-clamped support conditions due to the structure's stiffening.

Keywords

References

  1. Abdullah, S.S., Hashemi, S.H., Hussein, N.A. and Nazemnezhad, R. (2020), "Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium", J. Therm. Stress., 43(10), 1316-1332. https://doi.org/10.1080/01495739.2020.1780175.
  2. Akkoca, S., Bagdatli, S.M. and Togun, N.K. (2021), "Linear vibration movements of the mid-supported micro beam", J. Facult. Eng. Arch. Gazi Univ., 36(2), 1089-1103. https://doi.org/10.17341/gazimmfd.734809
  3. Arda, M. and Aydogdu, M. (2018), "Longitudinal magnetic field effect on torsional vibration of carbon nanotubes", J. Comput. Appl. Mech., 49(2), 304-313. https://doi.org/10.22059/jcamech.2018.269982.344.
  4. Arefi, M. and Zenkour, A.M. (2018), "Size-dependent vibration and electro-magneto-elastic bending responses of sandwich piezomagnetic curved nanobeams", Steel Compos. Struct., 29, 579-590. https://doi.org/10.12989/scs.2018.29.5.579.
  5. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low Dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014.
  6. Baghani, M., Mohammadi, M. and Farajpour, A. (2016), "Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy", Int. J. Appl. Mech., 8, 4. https://doi.org/10.1142/S1758825116500484.
  7. Bakhtiari, I., Behrouz, S.J. and Rahmani, O. (2020), "Nonlinear forced vibration of a curved micro beam with a surface-mounted light-driven actuator", Commun. Nonlin. Sci. Numer. Simul., 91, 105420. https://doi.org/10.1016/j.cnsns.2020.105420.
  8. Barati, A., Hadi, A., Nejad, M.Z. and Noroozi, R. (2020), "On vibration of bi-directional functionally graded nanobeams under magnetic field", Mech. Bas. Des. Struct. Mach., 1-18. https://doi.org/10.1080/15397734.2020.1719507.
  9. Behrouz, S.J., Rahmani, O. and Hossein, S.A. (2019), "On nonlinear forced vibration of nano cantilever-based biosensor via couple stress theory", Mech. Syst. Signal Pr., 128, 19-36. https://doi.org/10.1016/j.ymssp.2019.03.020.
  10. Cajic, M., Lazarevic, L., Karlici, D., Sun, H. and Liu, X. (2018), "Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles", Acta Mech., 229, 4791-4815. https://doi.org/10.1007/s00707-018-2263-7.
  11. Cajic, M.S., Lazarevic, M.P. and Karlicic, D.Z. (2015), "Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method", Proceedings of the 8th GRACM International Congress on Computational Mechanics, July.
  12. Chang, T. (2015), "Large amplitude free vibration of nanobeams subjected to magnetic field based on nonlocal elasticity theory", Appl. Mech. Mater., 764-765, 1199-1203, https://doi.org/10.4028/www.scientific.net/AMM.764-765.1199.
  13. Chang, T.P. (2016) "Nonlinear free vibration analysis of nanobeams under magnetic field based on nonlocal elasticity theory", J. Vibroeng., 18(3), http://doi.org/10.21595/jve.2015.16751.
  14. Ebrahimi, F. and Barati, M.R. (2016), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177/1077546316646239.
  15. Ebrahimi, F. and Barati, M.R. (2017), "Free vibration analysis of couple stress rotating nanobeams with surface effect under inplane axial magnetic field", J. Vib. Control, 24(21), 5097-5107. https://doi.org/10.1177/1077546317744719.
  16. Ebrahimi, F. and Barati, M.R. (2018), "Axial magnetic field effects on dynamic characteristics of embedded multiphase nanocrystalline nanobeams", Microsyst. Technol., 24, 3521-3536. https://doi.org/10.1007/s00542-018-3771-z.
  17. Ebrahimi, F. and Barati, M.R. (2018), "Nonlocal and surface effects on vibration behavior of axially loaded flexoelectric nanobeams subjected to in-plane magnetic field", Arab. J. Sci. Eng., 43, 1423-1433. https://doi.org/10.1007/s13369-017-2943-y.
  18. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  19. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  20. Hosseini, M. and Goughari, M.S. (2016), "Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field", Appl. Math. Model., 40(4), 2560-2576. https://doi.org/10.1016/j.apm.2015.09.106.
  21. Jandaghian, A. and Rahmani, O. (2017), "Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions", Steel Compos. Struct., 25(1), 67-78. https://doi.org/10.12989/scs.2017.25.1.067.
  22. Jandaghian, A.A. and Rahmani, O. (2016), "Free vibration analysis of magneto-electrothermo-elastic nanobeams resting on a Pasternak foundation", Smart Mater. Struct., 25, 035023. https://doi.org/10.1088/0964-1726/25/3/035023.
  23. Jena, S.K., Chakraverty, S. and Malikan, M. (2020), "Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler-Pasternak elastic foundation using a new refined beam theory: An analytical approach", Eur. Phys. J. Plus, 135, 164. https://doi.org/10.1140/epjp/s13360-020-00176-3
  24. Karlicic, D., Jovanovic, D., Kozic, P. and Cajic, M. (2015), "Thermal and magnetic effects on the vibration of a cracked nanobeam embedded in an elastic medium". J. Mech. Mater. Struct., 10, 43-62. https://doi.org/10.2140/jomms.2015.10.43.
  25. Murmu, T., McCarthy, M.A. and Adhikari, S. (2012), "Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems", J. Appl. Phys., 111, 113511. http://doi.org/10.1063/1.4720084
  26. Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, John Wiley, New York, USA.
  27. Rahmani, O. and Asemani, S.S. (2020), "Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories", Struct. Eng. Mech., 74(2), 175-187. http://doi.org/10.12989/sem.2020.74.2.175.
  28. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  29. Refaeinejad, V., Rahmani, O. and Hosseini, S.A.H. (2017), "An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories", Scientia Iranica., 24(3), 1635-1653. https://doi.org/10.24200/sci.2017.4141
  30. Sari, M.S. (2016), "Superharmonic resonance analysis of nonlocal nano beam subjected to axial thermal and magnetic forces and resting on a nonlinear elastic foundation", Microsyst. Technol., 23(8), 3319-3330. https://doi.org/10.1007/s00542-016-3161-3.
  31. Shojaeefard, M.H., Googarchin, H.S., Mahinzare, M. and Eftekhari S.A. (2018), "Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: A comparative study on modified couple stress theory and nonlocal elasticity theory", J. Intel. Mater. Syst. Struct., 29(11), 2492-2507. https://doi.org/10.1177/1045389X18770875.
  32. Sobhy, M. and Zenkour, A.M. (2018), "Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate", Compos. Part B: Eng., 154(1), 492-506. https://doi.org/10.1016/j.compositesb.2018.09.011.
  33. Stamenkovic, M.B., Karlicic, D., Janevski, G. and Kozic, P. (2016), "Nonlocal forced vibration of a double single-walled carbon nanotube system under the influence of an axial magnetic field", J. Mech. Mater. Struct., 11(3), 279-307. https://doi.org/10.2140/jomms.2016.11.279.
  34. Sun, X., Hong, Y., Dai, H. and Wang, L. (2017), "Nonlinear frequency analysis of buckled nanobeams in the presence of longitudinal magnetic field", Acta Mechanica Solida Sinica, 30(5), 465-473. https://doi.org/10.1016/j.camss.2017.08.002.
  35. Tang, Y. and Ding, Q. (2019), "Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads", Compos. Struct., 225, 111076. https://doi.org/10.1016/j.compstruct.2019.111076.
  36. Tang, Y. and Yang, T. (2018), "Bi-directional functionally graded nanotubes: fluid conveying dynamics", Int. J. Appl. Mech., 10(4), 1850041. https://doi.org/10.1142/S1758825118500412.
  37. Tang, Y., Lv, X. and Yang, T. (2019), "Bi-directional functionally graded beams: asymmetric modes and nonlinear free vibration", Compos. Part B, 156, 319-331. https://doi.org/10.1016/j.compositesb.2018.08.140.
  38. Tang, Y., Ma, Z.S., Ding, Q. and Wang, T. (2021) "Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: A nano-structure analysis", Compos. Struct., 264, 113746. https://doi.org/10.1016/j.compstruct.2021.113746.
  39. Tang, Y., Wang, T. and Zheng, Y. (2020), "Thermal effect on wave propagation behavior of viscoelastic carbon nanotubes conveying fluid with the spinning and longitudinal motions", Mod. Phys. Lett. B, 35(2), 2150052. https://doi.org/10.1142/S0217984921500524.
  40. Tang, Y., Zhong, S., Yang, T. and Ding, Q. (2019), "Interaction between thermal field and two-dimensional functionally graded materials: A structural mechanical example", Int. J. Appl. Mech., 11(10), 1950099. https://doi.org/10.1142/S1758825119500996.
  41. Yang, T., Tang, Y., Lid, Q. and Yang, X.D. (2018), "Nonlinear bending, buckling and vibration of bi-directional functionally graded nanobeams", Compos. Struct., 204, 313-319. https://doi.org/10.1016/j.compstruct.2018.07.045.
  42. Yapanmis, B.E., Bagdatli, S.M. and Togun, N. (2020), "Investigation of linear vibration behavior of middle supported nanobeam", El-Cezeri J. Sci. Eng., 7(3), 1450-1459. https://doi.org/10.31202/ecjse.741269.
  43. Zhao, D., Liu, Y. and Tang, Y. (2018), "Effects of magnetic field on size sensitivity of nonlinear vibration of embedded nanobeams", Mech. Adv. Mater. Struct., 26(11), 948-956. https://doi.org/10.1080/15376494.2018.1432783
  44. Zhen, Y., Wen, S. and Tang, Y. (2019), "Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model", Physica E: Low Dimens. Syst. Nanostruct., 105, 116-124. https://doi.org/10.1016/j.physe.2018.09.005.