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Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions

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Abstract

Based on the nonlocal strain gradient theory (NSGT), a model is proposed for an axially moving nanobeam with two kinds of scale effects. The internal resonance-accompanied fundamental harmonic response of the external excitation frequency in the vicinities of the first and second natural frequencies is studied by adopting the multivariate Lindstedt-Poincaré (L-P) method. Based on the root discriminant of the frequency-amplitude equation under internal resonance conditions, theoretical analyses are performed to investigate the scale effects of the resonance region and the critical external excitation amplitude. Numerical results show that the region of internal resonance is related to the amplitude of the external excitation. Particularly, the internal resonance disappears after a certain critical value of the external excitation amplitude is reached. It is also shown that the scale parameters, i.e., the nonlocal parameters and the material characteristic length parameters, respectively, reduce and increase the critical amplitude, leading to a promotion or suppression of the occurrence of internal resonance. In addition, the scale parameters affect the size of the enclosed loop of the bifurcated solution curves as well by changing their intersection, divergence, or tangency.

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Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu, 610500, China

    Jing Wang

  2. School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu, 610500, China

    Yilin Zhu

  3. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 611756, China

    Bo Zhang, Huoming Shen & Juan Liu

  4. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Chengdu, 611756, China

    Bo Zhang, Huoming Shen & Juan Liu

Authors
  1. Jing Wang
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  2. Yilin Zhu
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  3. Bo Zhang
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  4. Huoming Shen
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  5. Juan Liu
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Corresponding author

Correspondence to Yilin Zhu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11702036, 11602204, and 11502218)

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Wang, J., Zhu, Y., Zhang, B. et al. Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions. Appl. Math. Mech.-Engl. Ed. 41, 261–278 (2020). https://doi.org/10.1007/s10483-020-2565-5

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  • DOI: https://doi.org/10.1007/s10483-020-2565-5

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Chinese Library Classification

2010 Mathematics Subject Classification

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