Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory |
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| Institution: | 1. Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua, Mexico;2. Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV) Querétaro, Libramiento Norponiente 2000, Fracc. Real de Juriquilla, 76230 Querétaro, Mexico;3. Chernivtsi National University, Kotsyubynsky Str. 2, 58012 Chernivtsi, Ukraine;1. Instituto de Física, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia;2. Instituto de Física, Universidade Federal de Alagoas, Maceió-AL 57072-970, Brazil;3. Instituto de Física, Universidade Estadual de Campinas - Unicamp, Campinas - SP 13083-859, Brazil;1. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, NajafAbad, Najafabad, Iran;2. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran;3. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran;1. Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, B.P. 743, La Marsa, 2078, Tunisia;2. Department of Mechanical Engineering, Tunis Higher National Engineering School, University of Tunis, Tunis, 1008, Tunisia;3. Mechanical Engineering Program, Texas A&M University at Qatar, Engineering Building, P.O. Box 23874, Education City, Doha, Qatar;4. Department of Aerospace Engineering, Texas A&M University, College Station, TX, 77843, USA;5. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, PR China;1. School of Civil Engineering, University of Queensland, Queensland 4067, Australia;2. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China;3. Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge, Singapore 119260, Singapore;4. School of Engineering, RMIT University, PO Box 71, Bundoora, Victoria 3083, Australia |
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| Abstract: | In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model. |
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| Keywords: | Nanotube Nonlocal continuum theory Nonlinear vibration Parametric excitation Principal parametric resonances |
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