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Nonlinear dynamic response of beam and its application in nanomechanical resonator

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Abstract

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvature-dominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, 100190, Beijing, China

    Yin Zhang

  2. Faculty of Information and Automation, Kunming University of Science and Technology, 650051, Kunming, China

    Yun Liu

  3. Department of Mechanical Engineering, The University of Connecticut, Storrs, CT, 06269, USA

    Kevin D. Murphy

Authors
  1. Yin Zhang
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  2. Yun Liu
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  3. Kevin D. Murphy
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Corresponding author

Correspondence to Yin Zhang.

Additional information

The project was supported by the National Natural Science Foundation of China (10721202 and 11023001) and the Chinese Academy of Sciences (KJCX2-EW-L03).

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Zhang, Y., Liu, Y. & Murphy, K.D. Nonlinear dynamic response of beam and its application in nanomechanical resonator. Acta Mech Sin 28, 190–200 (2012). https://doi.org/10.1007/s10409-011-0501-5

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  • DOI: https://doi.org/10.1007/s10409-011-0501-5

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