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Thermally induced vibration of circular monolayer graphene considering quantum effects

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Abstract

Thermally induced axisymmetric and asymmetric vibrations of circular monolayer graphene considering quantum effects are studied using nonlocal elasticity theory. Explicit expressions are analytically developed for the root-mean-square (RMS) amplitude and the mode shape of thermal vibration. Following the expressions, the effects of nonlocal parameter, size, and temperature change of the circular graphene on the RMS amplitude and mode shape are explored. Results show that the RMS amplitude increases with increasing temperature and graphene size. In addition, the amplitude increases with an increase in the nonlocal parameter. For the mode (m, n) of thermal vibration of graphene, there are m − 1 nodal circles and n diametrical nodal lines. The sensors used to measure modal data can be placed at the diametrical nodal lines and nodal circles to avoid vibrational failure of the sensors.

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References

  1. Novoselov K.S., Geim A.K., Morozov S., Jiang D., Zhang Y., Dubonos S., Grigorieva I., Firsov A.: Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004)

    Article  Google Scholar 

  2. Meyer J.C., Geim A.K., Katsnelson M.I., Novoselov K.S., Booth T.J., Roth S.: The structure of suspended graphene sheets. Nature 446, 60–63 (2007)

    Article  Google Scholar 

  3. Ranjbartoreh A.R., Wang B., Shen X., Wang G.: Advanced mechanical properties of graphene paper. J. Appl. Phys. 109, 014306 (2011)

    Article  Google Scholar 

  4. Geim A.K., Novoselov K.S.: The rise of graphene. Nat. Mater. 6, 183–191 (2007)

    Article  Google Scholar 

  5. Stampfer C., Schurtenberger E., Molitor F., Guüttinger J., Ihn T., Ensslin K.: Tunable graphene single electron transistor. Nano Lett. 8, 2378–2383 (2008)

    Article  Google Scholar 

  6. Mueller T., Xia F., Avouris P.: Graphene photodetectors for high-speed optical communications. Nat. Photon. 4, 297–301 (2010)

    Article  Google Scholar 

  7. Cao G., Chen X., Kysar J.W.: Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes. J. Mech. Phys. Solids 54, 1206–1236 (2006)

    Article  MATH  Google Scholar 

  8. Wang L.F., Hu H.Y., Guo W.L.: Thermal vibration of carbon nanotubes predicted by beam models and molecular dynamics. Proc. R. Soc. Lond. Ser. A 466, 2325 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang L.F., Hu H.Y.: Thermal vibration of double-walled carbon nanotubes predicted via double-Euler-beam model and molecular dynamics. Acta Mech. 223, 2107–2115 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu R., Wang L.: Thermal vibration of a single-walled carbon nanotube predicted by semiquantum molecular dynamics. Phys. Chem. Chem. Phys. 17, 5194–5201 (2015)

    Article  Google Scholar 

  11. Chang W.J.: Molecular-dynamics study of mechanical properties of nanoscale copper with vacancies under static and cyclic loading. Microelectron. Eng. 65, 239–246 (2003)

    Article  Google Scholar 

  12. Fang T.H., Chang W.J., Feng Y.L.: Mechanical characteristics of graphene nanoribbons encapsulated in single-walled carbon nanotubes using molecular dynamics simulations. Appl. Surf. Sci. 356, 221–225 (2015)

    Article  Google Scholar 

  13. Wang L., Hu H.: Thermal vibration of single-walled carbon nanotubes with quantum effects. Proc. R. Soc. A 470, 20140087 (2014)

    Article  Google Scholar 

  14. Wang L., Hu H.: Thermal vibration of a rectangular single-layered graphene sheet with quantum effects. J. Appl. Phy. 115, 233515 (2014)

    Article  Google Scholar 

  15. Wang L., Hu H.: Thermal vibration of a circular single-layered graphene sheet with simply supported or clamped boundary. J. Sound Vib. 349, 206–215 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Lee H.L., Hsu J.C., Chang W.J.: Frequency shift of carbon-nanotube -based mass sensor using nonlocal elasticity theory. Nanoscale Res. Lett. 5, 1774–1778 (2010)

    Article  Google Scholar 

  18. Chang W.J., Lee H.L.: Mass detection using a double-layer circular graphene-based nanomechanical resonator. J. Appl. Phys. 116, 034303 (2014)

    Article  Google Scholar 

  19. Lee H.L., Chang W.J.: Thermally-induced asymmetric buckling of circular monolayer graphene. J. Nanomater. 2013, 416189 (2013)

    Google Scholar 

  20. Singh V., Sengupta S., Solanki H.S., Dhall R., Allain A., Dhara S., Pant P., Deshmukh M.M.: Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators. Nanotechnology 21, 165204 (2010)

    Article  Google Scholar 

  21. Murmu T., Adhikari S.: Nonlocal frequency analysis of nanoscale biosensors. Sensors Actuat. A 173, 41–48 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kun Shan University, Tainan, 71003, Taiwan

    Haw-Long Lee & Win-Jin Chang

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  1. Haw-Long Lee
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  2. Win-Jin Chang
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Correspondence to Win-Jin Chang.

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Lee, HL., Chang, WJ. Thermally induced vibration of circular monolayer graphene considering quantum effects. Acta Mech 227, 1067–1074 (2016). https://doi.org/10.1007/s00707-015-1510-4

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  • DOI: https://doi.org/10.1007/s00707-015-1510-4

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