Modelling the nonlinear behaviour of double walled carbon nanotube based resonator with curvature factors |
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| Institution: | 1. Physics Department, Faculty of Science and Science Education, School of Science, University of Sulaimani, Kurdistan Region, Iraq;2. Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland;3. Department of Mechanical Engineering, National United University, 1, Lienda, Miaoli 36003, Taiwan;4. School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland;1. Physics Department, Belarusian State University, pr. Nezavisimosti 4, Minsk 220030, Belarus;2. Institute for Spectroscopy Russian Academy of Science, Fizicheskaya Str. 5, Troitsk, 142190 Moscow, Russia;3. Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny, 141700 Moscow region, Russia;1. College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China;2. College of Optical and Electronic technology, China Jiliang University, Hangzhou, 310018, China;1. College of Physics and Electronics, Shandong Normal University, Jinan 250014, China;2. School of Physics, Shandong University, Jinan 250100, China;1. School of Civil Engineering, Shandong University, Jinan 250061, China;2. School of Mechanical Engineering, Shandong University, Jinan 250061, China;3. Research Center of Geotechnical and Structural Engineering, Shandong University, Jinan 250061, China |
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| Abstract: | This paper deals with the nonlinear vibration analysis of a double walled carbon nanotube based mass sensor with curvature factor or waviness, which is doubly clamped at a source and a drain. Nonlinear vibrational behaviour of a double-walled carbon nanotube excited harmonically near its primary resonance is considered. The double walled carbon nanotube is harmonically excited by the addition of an excitation force. The modelling involves stretching of the mid plane and damping as per phenomenon. The equation of motion involves four nonlinear terms for inner and outer tubes of DWCNT due to the curved geometry and the stretching of the central plane due to the boundary conditions. The vibrational behaviour of the double walled carbon nanotube with different surface deviations along its axis is analyzed in the context of the time response, Poincaré maps and Fast Fourier Transformation diagrams. The appearance of instability and chaos in the dynamic response is observed as the curvature factor on double walled carbon nanotube is changed. The phenomenon of Periodic doubling and intermittency are observed as the pathway to chaos. The regions of periodic, sub-harmonic and chaotic behaviour are clearly seen to be dependent on added mass and the curvature factors in the double walled carbon nanotube. Poincaré maps and frequency spectra are used to explicate and to demonstrate the miscellany of the system behaviour. With the increase in the curvature factor system excitations increases and results in an increase of the vibration amplitude with reduction in excitation frequency. |
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| Keywords: | Double walled carbon nanotube Nonlinear analysis Waviness Poincaré map Fast Fourier Transformation |
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