Skip to main content
SpringerLink
Log in

Nonlinear free vibration of core–shell nanowires with weak interfaces based on a refined nonlocal theory

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Based on a refined nonlocal theory, the nonlinear free vibration of core–shell nanowires is presented in this paper. This refined model can predict the weakening of interfacial bonding which satisfies the vanishing stress boundary condition at surface and stress continuity conditions at the interface. The nonlinear governing equations and boundary conditions are obtained by using Hamilton’s principle. The whole problem is solved by a second-step perturbation technique. In numerical results, the simply supported core–shell nanowire with inplane immovable is considered. The effects of transverse shear deformation, geometric sizes, and small-scale parameter and interfacial shear stiffness are discussed.

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

Similar content being viewed by others

References

  1. Lauhon, L.J., Gudiksen, M.S., Wang, C.L. et al.: Epitaxial core–shell and core–multishell nanowire heterostructures. Nature 420, 57–61 (2002)

    Article  Google Scholar 

  2. van Tilburg, J.W.W., Algra, R.E., Immink, W.G.G. et al.: Surface passivated InAs/InP core/shell nanowires. Semicond. Sci. Technol. 25, 024011 (2010)

    Article  Google Scholar 

  3. Qian, F., Gradecak, S., Li, Y. et al.: Core/multishell nanowire heterostructures as multicolor, high-efficiency light-emitting diodes. Nano Lett. 5, 2287–2291 (2005)

    Article  Google Scholar 

  4. Hayden, O., Greytak, A.B., Bell, D.C.: Core–shell nanowire light-emitting diodes. Adv. Mater. 17, 701–704 (2005)

    Article  Google Scholar 

  5. Liang, G.C., Xiang, J., Kharche, N. et al.: Performance analysis of a Ge/Si core/shell nanowire field-effect transistor. Nano Lett. 7, 642–646 (2007)

    Article  Google Scholar 

  6. Xiang, J., Lu, W., Hu, Y.J. et al.: Ge/Si nanowire heterostructures as high-performance field-effect transistors. Nature 441, 489–493 (2006)

    Article  Google Scholar 

  7. Cui, L.F., Ruffo, R., Chan, C.K. et al.: Crystalline–amorphous core–shell silicon nanowires for high capacity and high current battery electrodes. Nano Lett. 9, 491–495 (2009)

    Article  Google Scholar 

  8. Tian, B.Z., Zheng, X.L., Kempa, T.J. et al.: Coaxial silicon nanowires as solar cells and nanoelectronic power sources. Nature 449, 885–889 (2007)

    Article  Google Scholar 

  9. Chen, C.Q., Shi, Y., Zhang, Y.S. et al.: Size dependence of Young’s modulus in ZnO nanowires. Phys. Rev. Lett. 96, 075505 (2006)

    Article  Google Scholar 

  10. Duan, H.L., Weissmuller, J., Wang, Y.: Instabilities of core–shell heterostructured cylinders due to diffusions and epitaxy: spheroidization and blossom of nanowires. J. Mech. Phys. Solids 56, 1831–1851 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhu, H.X.: The effects of surface and initial stresses on the bending stiffness of nanowires. Nanotechnology 19, 405703 (2008)

    Article  Google Scholar 

  12. Skold, N., Karlsson, L.S., Larsson, M.W. et al.: Growth and optical properties of strained GaAs–Ga x In1-x P core–shell nanowires. Nano Lett. 5, 1943–1947 (2005)

    Article  Google Scholar 

  13. Gronqvist, J., Sondergaard, N., Boxberg, F. et al.: Strain in semiconductor core–shell nanowires. J. Appl. Phys. 106, 053508 (2009)

    Article  Google Scholar 

  14. Aifantis, K.E., Kolesnikova, A.L., Romanov, A.E.: Nucleation of misfit dislocations and plastic deformation in core/shell nanowires. Philos. Mag. 87, 4731–4757 (2007)

    Article  Google Scholar 

  15. Fu, Y., Zhang, P.: Buckling and vibration of core–shell nanowires with weak interfaces. Mech. Res. Commun. 37, 622–626 (2010)

    Article  MATH  Google Scholar 

  16. Fu, Y., Hong, J., Wang, X.: Analysis of nonlinear vibration for embedded carbon nanotubes. J. Sound Vib. 296, 746–756 (2006)

    Article  Google Scholar 

  17. Fu, Y., Wang, J., Hu, S.: Analytical solutions of thermal buckling and postbuckling of symmetric laminated composite beams with various boundary conditions. Acta Mech. 225, 13–29 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  18. Huang, Y., Li, X.F.: Bending and vibration of circular cylindrical beams with arbitrary radial nonhomogeneity. Int. J. Mech. Sci. 52, 595–601 (2010)

    Article  Google Scholar 

  19. Song, F., Huang, G.L., Varadan, V.K.: Study of wave propagation in nanowires with surface effects by using a high-order continuum theory. Acta Mech. 209, 129–139 (2010)

    Article  MATH  Google Scholar 

  20. Wang, G.-F., Feng, X.-Q.: Timoshenko beam model for buckling and vibration of nanowires with surface effects. J. Phys. D: Appl. Phys. 42, 155411 (2009)

  21. Chiu, M.-S., Chen, T.: Effects of high-order surface stress on buckling and resonance behavior of nanowires. Acta Mech. 223, 1473–1484 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  22. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)

    Article  Google Scholar 

  23. Yang, F., Chong, A., Lam, D. et al.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)

    Article  MATH  Google Scholar 

  24. Lam, D., Yang, F., Chong, A. et al.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  27. Narendar, S., Gopalakrishnan, S.: Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory. Acta Mech. 223, 395–413 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. Hutchinson, J.R.: Shear coefficients for Timoshenko beam theory. J. Appl. Mech. 68, 87–92 (2001)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  30. Wang, G.-F., Feng, X.-Q.: Surface effects on buckling of nanowires under uniaxial compression. Appl. Phys. Lett. 94, 141913 (2009)

    Article  Google Scholar 

  31. Shen, H.-S., Xiang, Y.: Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Eng. Struct. 56, 698–708 (2013)

    Article  Google Scholar 

  32. Shen, H.-S.: A two-step perturbation method in nonlinear analysis of beams, plates and shells. Wiley, Singapore (2013)

    Book  MATH  Google Scholar 

  33. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139–147 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Yiming Fu & Jun Zhong

Authors
  1. Yiming Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Zhong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, Y., Zhong, J. Nonlinear free vibration of core–shell nanowires with weak interfaces based on a refined nonlocal theory. Acta Mech 226, 1369–1377 (2015). https://doi.org/10.1007/s00707-014-1257-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1257-3

Keywords

Search

Navigation