Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method |
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| Institution: | 1. College of chemistry and materials engineering, Hainan Vocational University of Science and Technology, Haikou 571126, Hainan, China;2. Department of Civil Engineering, Calut Company Holding, Melbourne 3800, Australia;3. Department of Civil Engineering Discipline, School of Engineering, Monash University, Melbourne 3800, Australia;4. Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia;5. Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia |
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| Abstract: | Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions. |
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| Keywords: | Curved carbon nanotubes Geometric nonlinearity Van der Waals nonlinearity Differential quadrature method Euler–Bernoulli theory |
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