Jump to ContentJump to Main Navigation
Show Summary Details

Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

4 Issues per year

SCImago Journal Rank (SJR) 2015: 0.178
Source Normalized Impact per Paper (SNIP) 2015: 0.453
Impact per Publication (IPP) 2015: 0.314

Open Access
See all formats and pricing

Free Vibration of Piezo-Nanowires Using Timoshenko Beam Theory with Consideration of Surface and Small Scale Effects

Atta Oveisi
  • School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
  • :
Published Online: 2014-05-17 | DOI: https://doi.org/10.2478/meceng-2014-0008


This paper investigates the influence of surface effects on free transverse vibration of piezoelectric nanowires (NWs). The dynamic model of the NW is tackled using nonlocal Timoshenko beam theory. By implementing this theory with consideration of both non-local effect and surface effect under simply support boundary condition, the natural frequencies of the NW are calculated. Also, a closed form solution is obtained in order to calculate fundamental buckling voltage. Finally, the effect of small scale effect on residual surface tension and critical electric potential is explored. The results can help to design piezo-NW based instruments.


W pracy badano wpływ efektów powierzchniowych na poprzeczne drgania swobodne nanodrutów piezoelektrycznych (nanowires, NW). Model dynamiczny NW stworzono posługujac sie nielokalna teoria belki Timoszenki. Stosujac te teorie, przy uwzglednieniu zarówno efektów powierzchniowych i efektów nielokalnych, obliczono czestotliwosci drgan własnych nanodrutu. Uzyskane rozwiazanie, o formie zamknietej, pozwala takze obliczyc podstawowe napiecie wyboczenia. Ponadto, zbadano wpływ efektów małej skali na resztkowe naprezenie powierzchniowe i potencjał elektryczny. Wyniki pracy moga byc uzyteczne przy projektowaniu przyrzadów wykorzystujacych nanodruty piezoelektryczne.

Keywords : piezoceramic nanobeams; free vibrations; buckling; surface stress; non-local elasticity


  • [1] Wu G., Ji H., Hansen K., Thundat T., Datar R., Cote R., Hagan M.F., Chakraborty A.K., Majumdar A.: Origin of nanomechanical cantilever motion generated from biomolecular interactions. Proc. Natl Acad. Sci. USA, 2001, pp. 1560-1564.

  • [2] Cui Y., Zhong Z.H., Wang D.L., WangW.U., Lieber C.M.: High performance silicon nanowire field effect transistors. Nano Letters, 2003, Vol.3, No. 2, pp. 149-152. [Crossref]

  • [3] Cuenot S., Fretigny C., Demoustier-Champagne S., Nysten B.: Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Physical review series B, 2004, Vol. 69, No. 16, 165410(1-5).

  • [4] Jing G.Y., Duan H.L., Sun X.M., Zhang Z.S., Xu J., Li Y.D., Wang J.X., Yu D.P.: Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Physical review series B, 2006, Vol. 73, No. 16, 235409(1-6).

  • [5] Wang Z.Q., Zhao Y.P., Huang Z.P.: The effects of surface tension on the elastic properties of nano structures. International journal of engineering science, 2010, Vol. 48, pp. 140-150. [Crossref]

  • [6] Khajeansari A., Baradaran G.H., Yvonnet J.: An explicit solution for bending of nanowires lying on Winkler-Pasternak elastic substrate medium based on the Euler-Bernoulli beam theory. International journal of engineering science, 2012, Vol. 52, pp. 115-128. [Web of Science] [Crossref]

  • [7] Song F., Huang G.L., Park H.S., Liu X.N.: continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses, International journal of solids and structures, 2011, Vol. 48, pp. 2154-2163

  • [8] Song F., Huang G.L.: Modeling of surface stress effects on bending behavior of nanowires: Incremental deformation theory. Physics letters A, 2009, Vol. 373, pp. 3969-3973. [Web of Science]

  • [9] Park H.S.: Surface stress effects on the critical buckling strains of silicon nanowires. Computational materials science, 2012, Vol. 51, pp. 396-401. [Crossref] [Web of Science]

  • [10] Olsson P.A.T., Park H.S.: Atomistic study of the buckling of gold nanowires. Acta materialia, 2011, Vol. 59, pp. 3883-3894. [Crossref] [Web of Science]

  • [11] Gheshlaghi B., Hasheminejad S.M.: Surface effects on nonlinear free vibration of nanobeams, Composites: part B, 2011, Vol. 42, pp. 934-937. [Crossref] [Web of Science]

  • [12] Yao H., Yun G.: The effect of nonuniform surface elasticity on buckling of ZnO nanowires. Physica E, 2012, Vol. 44, pp. 1916-1919. [Crossref] [Web of Science]

  • [13] Gheshlaghi B., Hasheminejad S.M.: Adsorption-induced resonance frequency shift in Timoshenko microbeams. Current Applied physics, 2011, Vol. 11, pp. 1035-1041. [Web of Science] [Crossref]

  • [14] Gheshlaghi B., Hasheminejad S.M.: Vibration analysis of piezoelectric nanowires with surface and small scale effects. Current applied physics, 2012, Vol. 12, pp. 1096-1099. [Crossref]

  • [15] Wang G.F., Feng X.Q.: Timoshenko beam model for buckling and vibration of nanowires with surface effects. Journal of physics D: applied physics, 2009, Vol. 42, 155411(1-5).

  • [16] Yan Z., Jiang L.Y.: The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology, 2011, Vol. 22, 245703(1-7). [Web of Science]

  • [17] Zhan H.F., Gu Y.T.: Surface effects on the dual-mode vibration of 110 silver nanowires with different cross-sections, Journal of physics D: applied physics, 2012, Vol. 45, 465304(1-10).

  • [18] Wang G.F., Feng X.Q.: Effect of surface stresses on the vibration and buckling of piezoelectric nanowires. EPL, 2010, Vol. 91, 56007(1-4). [Web of Science]

  • [19] Jia-Hong Z., Xiao-Li M., Qing-Quan L., Fang G., Min L., Heng L., Yi-Xian G.: Mechanical properties of silicon nanobeams with an undercut evaluated by combining the dynamic resonance test and finite element analysis. Chinese physics B, 2012, Vol. 21, No. 8, 086101.

  • [20] He J., Lilley C.M.: Surface stress effect on bending resonance of nanowires with different boundary conditions. Applied physics letters, 2008, Vol. 93, 263108(1-3).

  • [21] Wang G.F., Feng X.Q.: Surface effects on buckling of nanowires under uniaxial compression. Applied physics letters, 2009, Vol. 94, 141913(1-3). [Web of Science]

  • [22] Hasheminejad S.M., Gheshlaghi B.: Dissipative surface stress effects on free vibrations of nanowires. Applied physics letters, 2010, Vol. 97, 253103(1-3).

  • [23] Olsson P.A.T, Park H.S., Lidstr¨om P.C.: The Influence of shearing and rotary inertia on the resonant properties of gold nanowires. Journal of applied physics, 2010, Vol. 108, 104312(1-9).

  • [24] Zhan H.F., Gu Y.T.: Modified beam theories for bending properties of nanowires considering surface/intrinsic effects and axial extension effect. Journal of applied physics, 2012, Vol. 111, 084305(1-9).

  • [25] Cha S.N., Seo J.S., Kim S.M., Kim H.J., Park Y.J., Kim S.W., Kim J.M.: Sound-driven piezoelectric nanowire based nanogenerators, Advanced materials, 2010, Vol. 22, pp. 4726-4730. [Crossref] [Web of Science]

  • [26] Gao Y.F.,Wang Z.L.: Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics, Nano letters, 2007, Vol. 7, pp. 2499-2505. [Web of Science] [Crossref]

  • [27] Cady W.G.: Piezoelectriciry, New York, McGraw-Hill Book Company Inc., 1946.

  • [28] Reddy J.N.: Energy Principles and Variational Methods in Applied Mechanics, second ed., New York, John Wiley & Sons, 2002.

  • [29] Reddy J.N.: Theory and Analysis of Elastic Plates and Shells, second ed., Philadelphia Taylor & Francis, 2007.

  • [30] Eringen A.C.: Nonlocal polar elastic continua, International journal of engineering science, 1972, Vol. 10, pp. 1-16. [Crossref]

  • [31] Eringen A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of applied physics, 1983, Vol. 54, pp. 4703-4710. [Crossref]

  • [32] Eringen A.C.: Nonlocal Continuum Field Theories, New York, Springer-Verlag, 2002.

  • [33] Wang G.F., Feng X.Q.: Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Applied physics letters, 2007, Vol. 90, 231904(1-3). [Web of Science]

  • [34] Shenoy V.B.: Size dependence of thermal expansion of nanostructures. Physical review series B, 2005, Vol. 71, 0941041-0941044.

Received: 2013-11-26

Published Online: 2014-05-17

Published in Print: 2014-03-01

Citation Information: Archive of Mechanical Engineering. Volume 61, Issue 1, Pages 139–152, ISSN (Online) 2300-1895, DOI: https://doi.org/10.2478/meceng-2014-0008, May 2014

© by Atta Oveisi. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Comments (0)

Please log in or register to comment.