Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory |
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Authors: | Bo Fang Ya-Xin Zhen Chi-Ping Zhang Ye Tang |
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Institution: | 1. School of Astronautics, Harbin Institute of Technology, P.O. Box 137, Harbin 150001, PR China;2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China |
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Abstract: | The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Kármán type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces. |
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Keywords: | Geometric nonlinearity Nonlinear van der Waals forces Nonlocal elasticity theory Harmonic balance method |
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