Current Applied Physics

Korean Physical Society (한국물리학회)
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Longitudinal vibration of cracked nanobeams using nonlocal elasticity theory

Hsu, Jung-Chang;Lee, Haw-Long;Chang, Win-Jin

  • Published : 20111100
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Abstract

The aim of this paper is to study the longitudinal frequency of a cracked nanobeam. The frequency equation of the nanobeam with clamped-clamped and clamped-free boundary conditions is derived based on the nonlocal elasticity theory. According to the equation, it can be found that the effects of the crack parameter, crack location, and nonlocal parameter on the longitudinal frequency of the cracked nanobeam are significant. The frequency decreases with an increase of the crack parameter. However, the increasing nonlocal parameter results in a decrease of the crack effect on the frequency. In addition, when the crack location is near the support, a larger decrease in the frequency can be observed.

Keywords

References

  1. E.V. Dirote (Ed.), Trends in Nanotechnology Research, Nova Science Publishers, New York, 2004.
  2. W.J. Chang, T.H. Fang, J. Phys. Chem. Solids 64 (2003) 1279. https://doi.org/10.1016/S0022-3697(03)00130-6
  3. T.H. Fang, W.J. Chang, S.L. Lin, Appl. Surf. Sci. 253 (2006) 1649. https://doi.org/10.1016/j.apsusc.2006.02.062
  4. D.L. Chen, T.C. Chen, Y.S. Lai, Nanoscale Res. Lett. 5 (2010) 315. https://doi.org/10.1007/s11671-009-9482-8
  5. A.C. Eringen, J. Appl. Phys. 54 (1983) 4703. https://doi.org/10.1063/1.332803
  6. H.L. Lee, W.J. Chang, J. Appl. Phys. 103 (2008) 024302. https://doi.org/10.1063/1.2822099
  7. H.L. Lee, W.J. Chang, J. Phys. Condens. Matter 21 (2009) 115302. https://doi.org/10.1088/0953-8984/21/11/115302
  8. H.L. Lee, W.J. Chang, Physica E 41 (2009) 529. https://doi.org/10.1016/j.physe.2008.10.002
  9. W.J. Chang, J.C. Hsu, H.L. Lee, Nanoscale Res. Lett. 5 (2010) 1774. https://doi.org/10.1007/s11671-010-9709-8
  10. M. Kirkham, Z.L. Wang, R.L. Snyder, Nanotechnology 19 (2008) 445708. https://doi.org/10.1088/0957-4484/19/44/445708
  11. Y. Sun, J. Gao, R. Zhu, J. Xu, L. Chen, J. Zhang, Q. Zhao, D. Yu, J. Chem. Phys. 132 (2010) 124705. https://doi.org/10.1063/1.3370339
  12. N. Pugno, Curr. Top. Acoust. Res. 4 (2006) 11.
  13. N. Pugno, Key Eng. Mater. 347 (2007) 199. https://doi.org/10.4028/www.scientific.net/KEM.347.199
  14. J. Loya, J. Lppez-Puente, R. Zaera, J. Fernandez-Saez, J. Appl. Phys. 105 (2009) 044309. https://doi.org/10.1063/1.3068370
  15. A. Morassi, J. Sound Vib. 242 (2001) 577. https://doi.org/10.1006/jsvi.2000.3380
  16. M. Aydogdu, Physica E 41 (2009) 861. https://doi.org/10.1016/j.physe.2009.01.007
  17. K.V. Singh, Mech. Syst. Signal Proc. 23 (2009) 1870. https://doi.org/10.1016/j.ymssp.2008.05.009

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