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Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

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Abstract

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube (SWCNT) subjected to a harmonic load is investigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Bo Wang  (王 博), Zi-chen Deng  (邓子辰) & Kai Zhang  (张 凯)

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Zi-chen Deng  (邓子辰)

Authors
  1. Bo Wang  (王 博)
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  2. Zi-chen Deng  (邓子辰)
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  3. Kai Zhang  (张 凯)
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Corresponding author

Correspondence to Zi-chen Deng  (邓子辰).

Additional information

Project supported by the National Basic Research Program of China (No. 2011CB610300), the National Natural Science Foundation of China (Nos. 10972182, 11172239, and 10902089), the 111 Project of China (No.B07050), the Ph.D. Programs Foundation of Ministry of Education of China (No. 20106102110019), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802), and the Doctorate Foundation of Northwestern Polytechnical University (No.CX201224)

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Wang, B., Deng, Zc. & Zhang, K. Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory. Appl. Math. Mech.-Engl. Ed. 34, 269–280 (2013). https://doi.org/10.1007/s10483-013-1669-8

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  • DOI: https://doi.org/10.1007/s10483-013-1669-8

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2010 Mathematics Subject Classification

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