XU Xiao-jian1, DENG Zi-chen1. Surface Effects of AdsorptionInduced Resonance Analysis of Micro/Nanobeams via Nonlocal Elasticity[J]. Applied Mathematics and Mechanics, 2013, 34(1): 10-17. doi: 10.3879/j.issn.1000-0887.2013.01.002
Citation: XU Xiao-jian1, DENG Zi-chen1. Surface Effects of AdsorptionInduced Resonance Analysis of Micro/Nanobeams via Nonlocal Elasticity[J]. Applied Mathematics and Mechanics, 2013, 34(1): 10-17. doi: 10.3879/j.issn.1000-0887.2013.01.002

Surface Effects of AdsorptionInduced Resonance Analysis of Micro/Nanobeams via Nonlocal Elasticity

doi: 10.3879/j.issn.1000-0887.2013.01.002
  • Received Date: 2012-05-14
  • Rev Recd Date: 2012-11-22
  • Publish Date: 2013-01-15
  • The governing differential equation of micro/nanobeams with atom/molecule adsorption was derived in presence of surface effects using the nonlocal elasticity. The effects of nonlocal parameter, adsorption density and the surface parameter on resonant frequency of the micro/nanobeams were investigated. It is found that, in addition to the nonlocal parameter and surface parameter, the bending rigidity and the adsorptioninduced mass exhibit different behaviors with the increase of adsorption density depending on the adatom category and the substrate material.
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  • [1]
    Goeders K M,Colton J S,Bottomley L A. Microcantilevers: sensing chemical interactions via mechanical motion[J]. Chemical Reviews,2008,108(2):522-542.
    [2]
    Alvarez M, Lechuga L M. Microcantilever-based platforms as biosensing tools[J].Analyst,2010,135(5): 827-836.
    [3]
    Eom K,Park H S,Yoon D S, Kwon T.Nanomechanical resonators and their applications in biological/chemical detection: nanomechanics principles[J].Physics Reports,2011,503(4/5): 115-163.
    [4]
    Hagan M F, Majumdar A, Chakraborty A K. Nanomechanical forces generated by surface grafted DNA[J]. The Journal of Physical Chemistry B,2002,106(39): 10163-10173.
    [5]
    Dareing D W, Thundat T.Simulation of adsorption induced stress of a microcantilever sensor[J]. Journal of Applied Physics,2005,97(4): 043526:1-5.
    [6]
    Eom K,Kwon T Y,Yoon D S,Lee H L,Kim T S.Dynamical response of nanomechanical resonators to biomolecular interactions[J].Physical Review B,2007,76(11):113408:1-4.
    [7]
    Huang G Y, Gao W, Yu S W.Model for the adsorptioninduced change in resonance frequency of a cantilever[J].Applied Physics Letters,2006,89(4):043506:1-4.
    [8]
    Zang J, Liu F.Theory of bending of Si nanocantilevers induced by molecular adsorption: a modified Stoney formula for the calibration of nanomechanochemical sensors [J].Nanotechnology,2007,18(40):405501:1-4.
    [9]
    Zang J, Liu F.Modified Timoshenko formula for bending of ultrathin strained bilayer films[J].Applied Physics Letters,2008,92(2):021905:1-3.
    [10]
    Zhang J Q, Yu S W, Feng X Q, Wang G F.Theoretical analysis of adsorptioninduced microcantilever bending[J].Journal of Applied Physics,2008,103(9): 093506:1-6.
    [11]
    Zhang J Q, Yu S W, Feng X Q.Theoretical analysis of resonance frequency change induced by adsorption[J]. Journal of Physics D:Applied Physics,2008,41(12):125306:1-8.
    [12]
    Gheshlaghi B, Hasheminejad S M. Adsorptioninduced resonance frequency shift in Timoshenko microbeams[J].Current Applied Physics,2011,11(4):1035-1041.
    [13]
    Yi X, Duan H L. Surface stress induced by interactions of adsorbates and its effect on deformation and frequency of microcantilever sensors[J]. Journal of the Mechanics and Physics of Solids,2009,57(8):1254-1266.
    [14]
    Feng L, Gao F, Liu M, Wang S, Li L, Shen M, Wang Z. Investigation of the mechanical bending and frequency shift induced by adsorption and temperature using micro and nanocantilever sensors[J]. Journal of Applied Physics,2012,112(1): 013501:1-9.
    [15]
    Wang C M, Zhang Y Y, Xiang Y, Reddy J N. Recent studies on buckling of carbon nanotubes[J]. Applied Mechanics Reviews,2010,63(3): 030804-030818.
    [16]
    Eringen A.On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves[J]. Journal of Applied Physics,1983,54(9):4703-4710.
    [17]
    Peddieson J, Buchanan G R, McNitt R P. Application of nonlocal continuum models to nanotechnology[J].International Journal of Engineering Science,2003,41(3/5):305-312.
    [18]
    Wang Q, Zhou G Y, Lin K C. Scale effect on wave propagation of doublewalled carbon nanotubes[J].International Journal of Solids and Structures,2006,43(20):6071-6084.
    [19]
    Zhang Y Q, Liu G R, Wang J S. Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression[J]. Physical Review B,2004,70(20): 205430:1-6.
    [20]
    Zhang Y Q, Liu G R, Xie X Y. Free transverse vibrations of doublewalled carbon nanotubes using a theory of nonlocal elasticity[J]. Physical Review B,2005,71(19):195404:1-7.
    [21]
    Wang K F, Wang B L. The electromechanical coupling behavior of piezoelectric nanowires: surface and small-scale effects[J].EPL (Europhysics Letters),2012,97(6):66005:1-6.
    [22]
    Juntarasaid C, Pulngern T, Chucheepsakul S. Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity[J]. Physica E: Low-Dimensional Systems and Nanostructures,2012,46:68-76.
    [23]
    Lee H L, Chang W J. Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory[J]. Journal of Applied Physics,2010,108(9): 093503:1-3.
    [24]
    Lei XW, Natsuki T, Shi JX, Ni QQ. Surface effects on the vibrational frequency of doublewalled carbon nanotubes using the nonlocal Timoshenko beam model[J]. Composites Part B: Engineering,2011,43(1): 64-69.
    [25]
    Wang K F, Wang B L. Vibration of nanoscale plates with surface energy via nonlocal elasticity[J].Physica E: LowDimensional Systems and Nanostructures,2011,44(2): 448-453.
    [26]
    Gheshlaghi B,Hasheminejad S M.Vibration analysis of piezoelectric nanowires with surface and small scale effects[J].Current Applied Physics,2012,12(4):1096-1099.
    [27]
    Wang L. Vibration analysis of fluidconveying nanotubes with consideration of surface effects[J].Physica E: LowDimensional Systems and Nanostructures,2010,43(1): 437-439.
    [28]
    Wang G F, Feng X Q. Effects of surface elasticity and residual surface tension on the natural frequency of microbeams[J].Applied Physics Letters,2007,90(23):231904:1-3.
    [29]
    He J, Lilley C M. Surface stress effect on bending resonance of nanowires with different boundary conditions[J]. Applied Physics Letters,2008,93(26): 263108:1-3.
    [30]
    Shenoy V B. Atomistic calculations of elastic properties of metallic fcc crystal surfaces[J]. Physical Review B, 2005,71(9):094104:1-11.
    [31]
    Abbasion S, Rafsanjani A, Avazmohammadi R, Farshidianfar A. Free vibration of microscaled Timoshenko beams[J]. Applied Physics Letters,2009,95(14):143122:1-3.
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