Journal of Zhejiang University-SCIENCE A

, Volume 11, Issue 1, pp 34–42 | Cite as

Free vibration of pre-tensioned nanobeams based on nonlocal stress theory

  • C. W. LimEmail author
  • Cheng Li
  • Ji-lin Yu


The transverse free vibration of nanobeams subjected to an initial axial tension based on nonlocal stress theory is presented. It considers the effects of nonlocal stress field on the natural frequencies and vibration modes. The effects of a small scale parameter at molecular level unavailable in classical macro-beams are investigated for three different types of boundary conditions: simple supports, clamped supports and elastically-constrained supports. Analytical solutions for transverse deformation and vibration modes are derived. Through numerical examples, effects of the dimensionless nanoscale parameter and pre-tension on natural frequencies are presented and discussed.

Key words

Nanobeam Natural frequency Nonlocal stress Pre-tensioned Vibration mode 

CLC number



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Copyright information

© Zhejiang University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Building and ConstructionCity University of Hong KongKowloon, Hong Kong SARChina
  2. 2.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina

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