Effects of strain and higher order inertia gradients on wave propagation in single-walled carbon nanotubes |
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| Affiliation: | 1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi''an 710072, PR China;2. Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang’an University, Xi''an 710064, PR China;1. Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico;2. NSCL and Department of Physics and Astronomy, Michigan State University, E. Lansing, MI 48824-1321, USA;3. College of Optics & Photonics-CREOL, University of Central Florida, 32816, USA;1. Centro de Investigación en Física, Universidad de Sonora, Apdo. Postal 142, Hermosillo, Sonora 83190, Mexico;2. Centro de Investigación y Estudios Avanzados del IPN, Unidad Querétaro, Apdo. Postal 1-798, Querétaro, Querétaro 76001, Mexico;3. Centro de Investigación y Desarrollo Tecnológico en Electroquímica, Parque Tecnológico Querétaro Sanfandila, Pedro Escobedo, Querétaro C.P. 76703, Mexico;1. State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People''s Republic of China;2. Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People''s Republic of China;3. Jinan Institute of Quantum Technology, SAICT, Jinan 250101, People''s Republic of China |
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| Abstract: | Dispersion relation of single-walled carbon nanotubes (SWCNTs) is investigated. The governing equations of motion of SWCNTs are derived on the basis of the gradient shell model, which involves one strain gradient and one higher order inertia parameters in addition to two Lamé constants. The present shell model can predict wave dispersion in good agreement with those of molecular dynamic (MD) simulations available in the literature. The effects of two small scale parameters on the angular frequency and phase velocity in the longitudinal, torsional and radial directions are studied in detail. The numerical results show that the angular frequency and phase velocity increase with the increase of strain gradient parameter, whereas decrease with inertia gradient parameter increases. In addition, analytical expressions of the cut-off frequencies and asymptotic phase velocities are given. It is found that the number of cut-off frequencies is dependent on the circumferential wave number, and two asymptotic phase velocities exist for nonzero value of strain gradient parameter, while only one exists when the strain gradient parameter is excluded. |
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| Keywords: | Carbon nanotube Wave dispersion Gradient elasticity Shell model Small scale effect |
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