Skip to main content
SpringerLink
Log in

Surface effects on vibration analysis of elastically restrained piezoelectric nanobeams subjected to magneto-thermo-electrical field embedded in elastic medium

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

In the present study, a generalized nonlocal beam theory is utilized to study the magneto–thermo–mechanical vibration characteristic of piezoelectric nanobeam by considering surface effects rested in elastic medium for various elastic boundary conditions. The nonlocal elasticity of Eringen as well as surface effects, including surface elasticity, surface stress and surface density are implemented to inject size-dependent effects into equations. Using the Hamilton’s principle and Euler–Bernoulli beam theory, the governing differential equations and associated boundary conditions will be obtained. The differential transformation method (DTM) is used to discretize resultant motion equations and related boundary conditions accordingly. The natural frequencies are obtained for the various elastic boundary conditions in detail to show the significance of nonlocal parameter, external voltage, temperature change, surface effects, elastic medium, magnetic field and length of nanobeam. Moreover, it should be noted that by changing the spring stiffness at each end, the conventional boundary conditions will be obtained which are validated by well-known literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. H.G. Craighead, Nanoelectromechanical systems. Science 290, 1532–1535 (2000)

    Article  ADS  Google Scholar 

  2. S. Hosseini-Hashemi, I. Nahas, M. Fakher, R. Nazemnezhad, Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity. Acta Mech. 225, 1555–1564 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. A.C. Eringen, Nonlocal continuum field theories, (Springer Science & Business Media, Berlin, 2002)

    MATH  Google Scholar 

  4. R. Sourki, S. Hoseini, Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory. Appl. Phys. A 122, 1–11 (2016)

    Article  Google Scholar 

  5. E.C. Aifantis, Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)

    Article  Google Scholar 

  6. M. Gurtin, J. Weissmüller, F. Larche, A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)

    Article  ADS  Google Scholar 

  7. A.C. Eringen, Theory of micropolar plates. Z. für Angew. Math. und Phys. ZAMP 18, 12–30 (1967)

    Article  ADS  Google Scholar 

  8. A. Anjomshoa, Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory. Meccanica 48, 1337–1353 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Bakhtiari-Nejad, M. Nazemizadeh, Size-dependent dynamic modeling and vibration analysis of MEMS/NEMS-based nanomechanical beam based on the nonlocal elasticity theory. Acta Mech. 227, 1363–1379 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. L.-L. Ke, Y.-S. Wang, Z.-D. Wang, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory. Compos. Struct. 94, 2038–2047 (2012)

    Article  Google Scholar 

  11. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal. 57, 291–323 (1975)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. M.E. Gurtin, A.I. Murdoch, Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978)

    Article  MATH  Google Scholar 

  13. R. Nazemnezhad, S. Hosseini-Hashemi, Nonlinear free vibration analysis of Timoshenko nanobeams with surface energy. Meccanica 50, 1027–1044 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. A.T. Samaei, M. Bakhtiari, G.-F. Wang, Timoshenko beam model for buckling of piezoelectric nanowires with surface effects. Nanoscale Res. Lett. 7, 1–6 (2012)

    Article  Google Scholar 

  15. A. Assadi, B. Farshi, Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech. 222, 27–39 (2011)

    Article  MATH  Google Scholar 

  16. J. He, C.M. Lilley, Surface effect on the elastic behavior of static bending nanowires. Nano Lett. 8, 1798–1802 (2008)

    Article  ADS  Google Scholar 

  17. Y. Feng, Y. Liu, B. Wang, Finite element analysis of resonant properties of silicon nanowires with consideration of surface effects. Acta Mech. 217, 149–155 (2011)

    Article  MATH  Google Scholar 

  18. M. Korayem, A. Korayem, The effect of surfaces type on vibration behavior of piezoelectric micro-cantilever close to sample surface in a humid environment based on MCS theory. Appl. Phys. A 122, 771 (2016)

    Article  ADS  Google Scholar 

  19. M. Ece, M. Aydogdu, Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes. Acta Mech. 190, 185–195 (2007)

    Article  MATH  Google Scholar 

  20. L.-L. Ke, Y.-S. Wang, Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Mater. Struct. 21, 025018 (2012)

    Article  ADS  Google Scholar 

  21. C.W. Lim, R. Xu, Analytical solutions for coupled tension-bending of nanobeam-columns considering nonlocal size effects. Acta Mech. 223, 789–809 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Aydogdu, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Phys. E Low-Dimens. Syst. Nanostructures 41, 1651–1655 (2009)

    Article  ADS  Google Scholar 

  23. M. Şimşek, H. Yurtcu, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos. Struct. 97, 378–386 (2013)

    Article  Google Scholar 

  24. S. Hosseini, O. Rahmani, Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory. Meccanica 52, 1441–1457 (2017)

    Article  MathSciNet  Google Scholar 

  25. A. Ghorbanpour-Arani, A. Rastgoo, M. Sharafi, R. Kolahchi, A.G. Arani, Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems. Meccanica 51, 25–40 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  26. T. Natsuki, N. Matsuyama, Q.-Q. Ni, Vibration analysis of carbon nanotube-based resonator using nonlocal elasticity theory. Appl. Phys. A 120, 1309–1313 (2015)

    Article  ADS  Google Scholar 

  27. M. Arda, M. Aydogdu, Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity. Appl. Phys. A 122, 1–10 (2016)

    Article  Google Scholar 

  28. X.-W. Lei, T. Natsuki, J.-X. Shi, Q.-Q. Ni, Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model. Compos Part B Eng, 43 (2012) 64–69

    Article  Google Scholar 

  29. K. Wang, B. Wang, Vibration of nanoscale plates with surface energy via nonlocal elasticity. Phys. E Low-Dimens. Syst. Nanostructures, 44 448–453 (2011)

    Article  ADS  Google Scholar 

  30. F. Ebrahimi, M. Boreiry, Investigating various surface effects on nonlocal vibrational behavior of nanobeams. Appl. Phys. A 121, 1305–1316 (2015)

    Article  ADS  Google Scholar 

  31. M. Eltaher, F. Mahmoud, A. Assie, E. Meletis, Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams. Appl. Math. Comput. 224, 760–774 (2013)

    MathSciNet  MATH  Google Scholar 

  32. F. Mahmoud, M. Eltaher, A. Alshorbagy, E. Meletis, Static analysis of nanobeams including surface effects by nonlocal finite element. J. Mech. Sci. Technol. 26, 3555–3563 (2012)

    Article  Google Scholar 

  33. P. Malekzadeh, M. Shojaee, Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams. Compos Part B Eng 52, 84–92 (2013)

    Article  Google Scholar 

  34. F. Ebrahimi, G.R. Shaghaghi, M. Boreiry, A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions. Int. J. Struct. Stab. Dyn. 16, 155002 (2015)

    MathSciNet  MATH  Google Scholar 

  35. M. Ghadiri, N. Shafiei, A. Akbarshahi, Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam. Appl. Phys. A 122, 1–19 (2016)

    Google Scholar 

  36. M. Ghadiri, M. Soltanpour, A. Yazdi, M. Safi, Studying the influence of surface effects on vibration behavior of size-dependent cracked FG Timoshenko nanobeam considering nonlocal elasticity and elastic foundation. Appl. Phys. A 122, 1–21 (2016)

    Google Scholar 

  37. F. Ebrahimi, M.R. Barati, Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment. J. Vib. Control 1077546316646239 (2016)

  38. L. Ke, Y. Wang, J. Yang, S. Kitipornchai, Thermo-electric-mechanical vibration of nonlocal piezoelectric nanobeams, in: 4th International Conference on Dynamics, Vibration and Control (ICDVC2014), 2014

  39. M. Mohammadimehr, S.A.M. Managheb, S. Alimirzaei, Nonlocal buckling and vibration analysis of triple-walled zno piezoelectric timoshenko nano-beam subjected to magneto-electro-thermo-mechanical loadings. Mech. Adv. Compos. Struct. 2 113–126 (2015)

    Google Scholar 

  40. J. Marzbanrad, M. Boreiry, G.R. Shaghaghi, Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect. Appl. Phys. A 122, 1–14 (2016)

    Article  Google Scholar 

  41. R. Ansari, T. Pourashraf, R. Gholami, S. Sahmani, Postbuckling behavior of functionally graded nanobeams subjected to thermal loading based on the surface elasticity theory. Meccanica 52, 283–297 (2016)

    Article  MathSciNet  Google Scholar 

  42. M. Pakdemirli, H. Boyacı, Vibrations of a stretched beam with non-ideal boundary conditions. Math. Comput. Appl. 6 217–220 (2001)

    MATH  Google Scholar 

  43. M. Pakdemirli, H. Boyaci, Effect of non-ideal boundary conditions on the vibrations of continuous systems. J. Sound Vib. 249, 815–823 (2002)

    Article  ADS  Google Scholar 

  44. N. Wattanasakulpong, A. Chaikittiratana, On the linear and nonlinear vibration responses of elastically end restrained beams using DTM. Mech Based Des. Struct. Mach. 42 135–150 (2014)

    Article  Google Scholar 

  45. M. Zarepour, S.A. Hosseini, A semi analytical method for electro-thermo-mechanical nonlinear vibration analysis of nanobeam resting on the winkler-pasternak foundations with general elastic boundary conditions. Smart. Mater. Struct. 25, 085005 (2016)

    Article  ADS  Google Scholar 

  46. T. Murmu, S. Pradhan, Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Comput. Mater. Sci. 46, 854–859 (2009)

    Article  Google Scholar 

  47. K. Wang, B. Wang, The electromechanical coupling behavior of piezoelectric nanowires: surface and small-scale effects. EPL (Europhysics Letters) 97, 66005 (2012)

    Article  ADS  Google Scholar 

  48. J. Reddy, Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)

    Article  MATH  Google Scholar 

  49. I.A.-H. Hassan, Application to differential transformation method for solving systems of differential equations. Appl. Math. Modell. 32, 2552–2559 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  50. M. Eltaher, A.E. Alshorbagy, F. Mahmoud, Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Appl. Math. Modell. 37, 4787–4797 (2013)

    Article  MathSciNet  Google Scholar 

  51. R. Ansari, S. Sahmani, Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models. Commun. Nonlinear Sci. Numer. Simul. 17, 1965–1979 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  52. S. Hosseini–Hashemi, M. Fakher, R. Nazemnezhad, Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: a comparison between Euler-Bernoulli and Timoshenko. Journal of Solid Mechanics 5, 290–304 (2013)

    Google Scholar 

  53. M. Komijani, Y. Kiani, S. Esfahani, M. Eslami, Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams. Compos. Struct. 98, 143–152 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vehicle Dynamical Systems Research Laboratory, School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran

    Javad Marzbanrad

  2. Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Mahya Boreiry & Gholam Reza Shaghaghi

Authors
  1. Javad Marzbanrad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahya Boreiry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gholam Reza Shaghaghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Javad Marzbanrad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marzbanrad, J., Boreiry, M. & Shaghaghi, G.R. Surface effects on vibration analysis of elastically restrained piezoelectric nanobeams subjected to magneto-thermo-electrical field embedded in elastic medium. Appl. Phys. A 123, 246 (2017). https://doi.org/10.1007/s00339-017-0768-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-017-0768-x

Search

Navigation