Abstract
A semi-analytical method named Galerkin strip distributed transfer function method (GSDTFM) is employed to solve the buckling and vibration of a single-layered graphene sheet (SLGS) nanomechanical resonator subjected to initial in-plane loads within the framework of the nonlocal Kirchhoff plate theory. The buckling load and the frequency shift are obtained by using the GSDTFM. And the effects of the initial in-plane load, the nonlocal parameter as well as the attached nanoparticle location on the frequency shift are investigated. The simulated results show that the buckling load of the SLGS depends on not only the side length of the SLGS, but also the small scale effects. The impact of the initial in-plane load on the fundamental frequency is significant. The frequency shift at an initial tensile load is larger than that at an initial compressive load. These results are consistent with the previously reported ones.
Similar content being viewed by others
References
Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004)
Dresselhaus, M.S., Dresselhaus, G., Jorio, A.: Unusual properties and structure of carbon nanotubes. Ann. Rev. Mater. Res. 34, 247–278 (2004)
Wong, E.W., Sheehan, P.E., Lieber, C.M.: Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277, 1971–1975 (1997)
Poncharal, P., Wang, Z.L., Ugarte, D., Heer, W.: Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513–1516 (1999)
Li, C.Y., Chou, T.W.: Mass detection using carbon nanotube-based nanomechanical resonators. Appl. Phys. Lett. 84, 5246–5248 (2004)
Li, C.Y., Chou, T.W.: Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators. Phys. Rev. B 68, 073405 (2003)
Shen, Z.B., Tang, H.L., Li, D.K., Tang, G.J.: Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 61, 200–205 (2012)
Sakhaee-Pour, A., Ahmadian, M.T., Vafai, A.: Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors. Solid State Commun. 145, 168–172 (2008)
Sakhaee-Pour, A., Ahmadian, M.T., Vafai, A.: Potential application of single-layered graphene sheet as strain sensor. Solid State Commun. 147, 336–340 (2008)
Arash, B., Wang, Q., Duan, W.H.: Detection of gas atoms via vibration of graphenes. Phys. Lett. A 375, 2411–2415 (2011)
Arash, B., Wang, Q.: Detection of gas atoms with graphene sheets. Comput. Mater. Sci. 60, 245–249 (2012)
Eringen, A.C.: On differential equations of nonlocal elasticity and solution of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)
Pradhan, S.C., Phadikar, J.K.: Nonlocal elasticity theory for vibration of nanoplates. J. Sound Vib. 325, 206–223 (2009)
Sari, M., Al-Kouz, W.: Vibration analysis of non-uniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory. Int. J. Mech. Sci. 114, 1–11 (2016)
Lim, M.Z.I.C.W., Zhang, G.: A nonlocal finite element method for torsional statics and dynamics of circular nanostructures. Int. J. Mech. Sci. 94–95, 232–243 (2015)
Sarrami-Foroushani, S., Azhari, M.: Nonlocal buckling and vibration analysis of thick rectangular nanoplates using finite strip method based on refined plate theory. Acta Mech. 227, 721–742 (2016)
Li, X.F., Tang, G.J., Shen, Z.B., Lee, K.Y.: Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55, 75–84 (2015)
Zhou, S.M., Sheng, L.P., Shen, Z.B.: Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 86, 73–78 (2014)
Bedroud, M., Hosseini-Hashemi, S., Nazemnezhad, R.: Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity. Acta Mech. 224, 2663–2676 (2013)
Sari, M.S.: Free vibration analysis of non-local annular sector Mindlin plates. Int. J. Mech. Sci. 96–97, 25–35 (2015)
Wang, X., Cai, H.: Effects of initial stress on non-coaxial resonance of multi-wall carbon nanotubes. Acta Mater. 54, 2067–2074 (2006)
Timoshenko, S.P., Woinowsky-Krieger, S.: Theory of Plates and Shells. McGraw-Hill, New York (1959)
Shen, Z.B., Tang, G.J., Zhang, L., Li, X.F.: Vibration of double-walled carbon nanotube based nanomechanical sensor with initial axial stress. Comput. Mater. Sci. 58, 51–58 (2012)
Heireche, H., Tounsi, A., Benzair, A.: Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading. Nanotechnology 19, 185703 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, R.W., Shen, Z.B. & Tang, G.J. A semi-analytical method for nonlocal buckling and vibration of a single-layered graphene sheet nanomechanical resonator subjected to initial in-plane loads. Acta Mech 228, 1725–1734 (2017). https://doi.org/10.1007/s00707-016-1795-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-016-1795-y