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

doi:10.1007/s10483-020-2565-5

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (2): 261-278.doi: https://doi.org/10.1007/s10483-020-2565-5

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

Jing WANG¹, Yilin ZHU², Bo ZHANG^3,4, Huoming SHEN^3,4, Juan LIU^3,4

1. School of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu 610500, China;
2. School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu 610500, China;
3. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 611756, China;
4. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Chengdu 611756, China

收稿日期:2019-06-11 修回日期:2019-09-10 发布日期:2020-01-03
通讯作者: Yilin ZHU E-mail:lin5210feng@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702036, 11602204, and 11502218)

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

Jing WANG¹, Yilin ZHU², Bo ZHANG^3,4, Huoming SHEN^3,4, Juan LIU^3,4

1. School of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu 610500, China;
2. School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu 610500, China;
3. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 611756, China;
4. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Chengdu 611756, China

Received:2019-06-11 Revised:2019-09-10 Published:2020-01-03
Contact: Yilin ZHU E-mail:lin5210feng@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702036, 11602204, and 11502218)

摘要/Abstract

摘要： 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 resonanceaccompanied 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 frequencyamplitude 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.

关键词: scale effect, axially moving nanobeam, internal resonance, critical amplitude

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 resonanceaccompanied 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 frequencyamplitude 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.

Key words: scale effect, axially moving nanobeam, internal resonance, critical amplitude

中图分类号:

74H45

Jing WANG, Yilin ZHU, Bo ZHANG, Huoming SHEN, Juan LIU. Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 261-278.

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

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

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