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Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method

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Abstract

The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory. The governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam. The method of multiple scales is applied to the governing equation to evaluate the nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and highlight the contributions of the nonlinear term and nonlocal effect.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang, 110136, China

    XiaoDong Yang

  2. Department of Building and Construction, City University of Hong Kong, Hong Kong, 999077, China

    C. W. Lim

Authors
  1. XiaoDong Yang
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  2. C. W. Lim
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Corresponding author

Correspondence to XiaoDong Yang.

Additional information

Supported by the Collaboration Scheme from University of Science and Technology of China-City University of Hong Kong Joint Advanced Research Institute and the National Natural Science Foundation of China (Grant No. 10702045)

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Yang, X., Lim, C.W. Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method. Sci. China Ser. E-Technol. Sci. 52, 617–621 (2009). https://doi.org/10.1007/s11431-009-0046-z

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  • DOI: https://doi.org/10.1007/s11431-009-0046-z

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