Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic characteristics of hygro-magneto-thermo-electrical nanobeam with non-ideal boundary conditions

  • Ebrahimi, Farzad (Mechanical Engineering Department, Engineering Faculty, Imam Khomeini International University) ;
  • Kokaba, Mohammadreza (Mechanical Engineering Department, Engineering Faculty, Imam Khomeini International University) ;
  • Shaghaghi, Gholamreza (Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University) ;
  • Selvamani, Rajendran (Department of Mathematics, Karunya University)
  • Received : 2019.04.05
  • Accepted : 2020.01.19
  • Published : 2020.02.25
⟨ Previous Next ⟩

Abstract

This study presents the hygro-thermo-electromagnetic mechanical vibration attributes of elastically restrained piezoelectric nanobeam considering effects of beam surface for various elastic non-ideal boundary conditions. The nonlocal Eringen theory besides the surface effects containing surface stress, surface elasticity and surface density are employed to incorporate size-dependent effects in the whole of the model and the corresponding governing equations are derived using Hamilton principle. The natural frequencies are derived with the help of differential transformation method (DTM) as a semi-analytical-numerical method. Some validations are presented between differential transform method results and peer-reviewed literature to show the accuracy and the convergence of this method. Finally, the effects of spring constants, changing nonlocal parameter, imposed electric potential, temperature rise, magnetic potential and moisture concentration are explored. These results can be beneficial to design nanostructures in diverse environments.

Keywords

References

  1. 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
  2. Bailey, T. and Ubbard, J.E. (1985), "Distributed piezoelectricpolymer active vibration control of a cantilever beam", J. Guidance, Control, and Dynamics, 8(5), 605-611. https://doi.org/10.2514/3.20029
  3. Barari, A., Kaliji, H.D., Ghadimi, M. and Domairry, G. (2011), "Non-linear vibration of Euler-Bernoulli beams", Latin Am. J. Solids Struct., 8(2), 139-148. https://doi.org/10.1590/S1679-78252011000200002
  4. Bauchau, O.A. and Craig, J.I. (2009), "Euler-Bernoulli beam theory", In: Structural Analysis, Springer, pp. 173-221.
  5. Ebrahimi, F. and Barati, M.R. (2017), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936. https://doi.org/10.1080/15376494.2016.1196795
  6. Ebrahimi, F., Shaghaghi, G.R. and Salari, E. (2014), "Vibration analysis of size-dependent nano beams based on nonlocal Timoshenko Beam Theory", J. Mech. Eng. Technol. (JMET), 6(2).
  7. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Vibration analysis of Euler--Bernoulli nanobeams by using finite element method", Appl. Mathe. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  8. Eringen, A.C. (1983), "On differential equations 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
  9. Friesen, C., Dimitrov, N., Cammarata, R.C. and Sieradzki, K. (2001), "Surface stress and electrocapillarity of solid electrodes", Langmuir, 17(3), 807-815. https://doi.org/10.1021/la000911m
  10. Gayen, D. and Roy, T. (2013), "Hygro-thermal effects on stress analysis of tapered laminated composite beam", Int. J. Compos. Mater., 3(3), 46-55. https://doi.org/10.5923/j.cmaterials.20130303.02
  11. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Rational Mech. Anal., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  12. He, J. and Lilley, C.M. (2008), "Surface effect on the elastic behavior of static bending nanowires", Nano Lett., 8(7), 1798-1802. https://doi.org/10.1021/nl0733233
  13. Henderson, J.P., Plummer, A. and Johnston, N. (2018), "An electro-hydrostatic actuator for hybrid active-passive vibration isolation", Int. J. Hydromechatron., 1(1), 47-71. https://doi.org/10.1504/IJHM.2018.090305
  14. Hosseini-Hashemi, S., Fakher, M. and Nazemnezhad, R. (2013), "Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: A comparison between Euler-Bernoulli and Timoshenko", J. Solid Mech., 5(3), 290-304.
  15. Huang, G.-Y. and Yu, S.-W. (2006), "Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring", Physica Status Solidi (b), 243(4). https://doi.org/10.1002/pssb.200541521
  16. Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", Computati. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002
  17. Komijani, M., Kiani, Y., Esfahani, S.E. and Eslami, M.R (2013), "Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams", Compos. Struct., 98, 143-152. https://doi.org/10.1016/j.compstruct.2012.10.047
  18. Lee, U. and Kim, J. (2000), "Determination of nonideal beam boundary conditions: a spectral element approach", AIAA Journal, 38(2), p. 309. https://doi.org/10.2514/2.958
  19. Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74(1), 81-87. https://doi.org/10.1016/0022-460X(81)90493-4
  20. Li, X.Y., Wang, Z.K. and Huang, S.H. (2004), "Love waves in functionally graded piezoelectric materials", Int. J. Solids Struct., 41(26), 7309-7328. https://doi.org/10.1016/j.ijsolstr.2004.05.064
  21. Marzbanrad, J., Boreiry, M. and Shaghaghi, G.R. (2016), "Thermo-electro-mechanical vibration analysis of sizedependent nanobeam resting on elastic medium under axial preload in presence of surface effect", Appl. Phys. A, 122(7), p. 691. https://doi.org/10.1007/s00339-016-0218-1
  22. Marzbanrad, J., Boreiry, M. and Shaghaghi, G.R. (2017), "Surface effects on vibration analysis of elastically restrained piezoelectric nanobeams subjected to magneto-thermo-electrical field embedded in elastic medium", Appl. Phys. A, 123(4), p. 246. https://doi.org/10.1007/s00339-017-0768-x
  23. Pakdemirli, M. and Boyaci, H. (2001), "Vibrations of a stretched beam with non-ideal boundary conditions", Mathe. Computat. Applicat., 6(3), 217-220. https://doi.org/10.3390/mca6030217
  24. Pakdemirli, M. and Boyaci, H. (2003), "Non-linear vibrations of a simple--simple beam with a non-ideal support in between", J. Sound Vib., 268(2), 331-341. https://doi.org/10.1016/S0022-460X(03)00363-8
  25. Park, S.K. and Gao, X.L. (2006), "Bernoulli--Euler beam model based on a modified couple stress theory", J. Micromech. Microeng., 16(11), p. 2355. https://doi.org/10.1088/0960-1317/16/11/015
  26. Rao, S.S. (2007), Vibration of Continuous Systems, John Wiley & Sons.
  27. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  28. Samaei, A.T., Bakhtiari, M. and Wang, G.-F. (2012), "Timoshenko beam model for buckling of piezoelectric nanowires with surface effects", Nanoscale Res. Lett., 7(1), p. 201. https://doi.org/10.1186/1556-276X-7-201
  29. Schmid, M., Hofer, W., Varga, P., Stoltze, P., Jacobsen, K.W. and No, J.K. (1995), "Surface stress, surface elasticity, and the size effect in surface segregation", Phys. Rev. B, 51(16), p. 10937. https://doi.org/10.1103/PhysRevB.51.10937
  30. Tanaka, Y. (2018), "Active vibration compensator on moving vessel by hydraulic parallel mechanism", Int. J. Hydromechatron., 1(3), 350-359. https://doi.org/10.1504/ijhm.2018.094887
  31. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  32. Wang, C.M., Tan, V.B.C. and Zhang, Y.Y. (2006), "Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes", J. Sound Vib., 294(4), 1060-1072. https://doi.org/10.1021/nl035198a
  33. Wang, Z., Xie, Z. and Huang, W. (2018), "A pin-moment model of flexoelectric actuators", Int. J. Hydromechatron., 1(1), 72-90. https://doi.org/10.1504/IJHM.2018.090306
  34. Zhao, M.-H., Wang, Z.-L. and Mao, S.X. (2004), "Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope", Nano Lett., 4(4), 587-590. https://doi.org/10.1021/nl035198a

Cited by

  1. Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.115