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Thermal Vibration of Carbon Nanostructures

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Handbook of Mechanics of Materials

Abstract

The chapter presents the study on thermal vibration of nanostructures, such as carbon nanotube (CNT) and graphene, as well as the basic finding for the relation between the temperature and the root-of-mean-square (RMS) amplitude of the thermal vibration of the carbon nanostructures. In this study, the molecular dynamics (MD) based on modified Langevin dynamics, which accounts for quantum statistics by introducing a quantum heat bath, is used to simulate the thermal vibration of carbon nanostructures. The simulations show that the RMS amplitude of the thermal vibration of the carbon nanostructures obtained from the semi-quantum MD is lower than that obtained from the classical MD, especially for very low temperature and high-order vibration modes. The RMS amplitudes of the thermal vibrations of the single-walled CNT (SWCNT) and graphene obtained from the semi-quantum MD coincide well with those from the models of Timoshenko beam and Kirchhoff plate with quantum effects. These results indicate that quantum effects are important for the thermal vibration of the SWCNT and graphene in the case of high-order vibration modes, small size, and low temperature. Furthermore, the thermal vibration of a simply supported SWCNT subject to thermal stress is investigated by using the models of planar and non-planar nonlinear beams, respectively. The whirling motion with energy transfer between flexural motions is found in the SWCNT when the geometric nonlinearity is significant. The energies of different vibration modes are not equal even over a time scale of tens of nanoseconds, which is much larger than the period of fundamental natural vibration of the SWCNT at equilibrium state. The energies of different modes become equal when the time scale increases to the range of microseconds.

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Author information

Authors and Affiliations

  1. State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Lifeng Wang, Haiyan Hu & Rumeng Liu

  2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China

    Haiyan Hu

  3. Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, Jiangnan University, Wuxi, China

    Rumeng Liu

Authors
  1. Lifeng Wang
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  2. Haiyan Hu
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  3. Rumeng Liu
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Corresponding author

Correspondence to Lifeng Wang .

Editor information

Editors and Affiliations

  1. Institute for Materials Testing, Materials Science and Strength of Materials, University of Stuttgart, Stuttgart, Germany

    Siegfried Schmauder

  2. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

    Chuin-Shan Chen

  3. UAB Mail BEC 254, Birmingham, AL, USA

    Krishan K. Chawla

  4. Fulton School of Engineering, Arizona State University , Tempe, AZ, USA

    Nikhilesh Chawla

  5. Engineering Mechanics, Zhejiang University , Hangzhou, China

    Weiqiu Chen

  6. Katayanagi Advanced Research Laboratories, Tokyo University of Technology, Tokyo, Japan

    Yutaka Kagawa

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© 2019 Springer Nature Singapore Pte Ltd.

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Wang, L., Hu, H., Liu, R. (2019). Thermal Vibration of Carbon Nanostructures. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6884-3_16

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