Early transient responses of multi-span stepped single-walled carbon nanotubes using the method of reverberation ray matrix |
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| Institution: | 1. P.O. Box 423, School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, PR China;2. School of Mechanical Engineering, Beijing University of Technology, Beijing 100124, PR China;1. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong, China;2. School of Mechanical Engineering, Beijing University of Technology, Beijing, PR China;1. Department of Mechanical Engineering, Hong Kong Polytechnic University, H.K. PR China;2. Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, PR China;3. The Institute of Sound and Vibration Research, University of Southampton, UK;4. School of Mechanical Engineering, Beijing University of Technology, Beijing, PR China;1. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong;2. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China;1. Department of Biophysics, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, PR China;2. Hospital of Chengdu University of Traditional Chinese Medicine, No. 39 Shi-er-qiao Road, Chengdu 610072, Sichuan, PR China;3. Center for Information in Biology, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, PR China;4. Department of Biomedical Engineering, Hong Kong Polytechnic University, Hong Kong, PR China |
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| Abstract: | The early transient responses of multi-span stepped single walled carbon nanotubes (SWCNTs) under impact loadings are studied by the method of reverberation ray matrix (MRRM). The dynamics model of the carbon nanotubes is established in the Fourier phase space on the basis of the nonlocal Timoshenko beam model. The wave solutions of SWCNTs with arbitrary boundary conditions are obtained by the wave method. The reverberation ray matrix of the multi-span stepped SWCNTs is the product of scattering, phase and permutation matrices, which can be determined by the impact loadings, continuous conditions and boundary conditions. The early transient responses can be calculated by the inverse Fourier transform of the sum of initial ray groups. It can be found that the early transient displacement response in the very short time subjected to the impact loading is very small, while the transient transverse shear strain becomes large in the very short time. The influences of nanotubes span number, nanotubes type and boundary conditions on the early transient responses of multi-span stepped SWCNTs are investigated. |
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| Keywords: | Carbon nanotubes Early transient response Wave propagation Reverberation ray matrix method |
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