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Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Received: 7 June 2016     Published: 8 June 2016
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Abstract

Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the excitation amplitude to the damping coefficient crosses a critical value, sub-harmonic bifurcations of m order (odd) can occur. The stability conditions of the bifurcation solution for the system parameters are also obtained by using the affection-angle transformation and average method. The result can provide some guidance for the design of this class of sensors.

Published in Applied and Computational Mathematics (Volume 5, Issue 3)
DOI 10.11648/j.acm.20160503.11
Page(s) 97-102
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Sub-harmonic Bifurcation, Carbon Nanotube, Sub-harmonic Melnikov Method, Stability

References
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    Liangqiang Zhou, Shanshan Liu, Fangqi Chen. (2016). Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor. Applied and Computational Mathematics, 5(3), 97-102. https://doi.org/10.11648/j.acm.20160503.11

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    ACS Style

    Liangqiang Zhou; Shanshan Liu; Fangqi Chen. Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor. Appl. Comput. Math. 2016, 5(3), 97-102. doi: 10.11648/j.acm.20160503.11

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    AMA Style

    Liangqiang Zhou, Shanshan Liu, Fangqi Chen. Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor. Appl Comput Math. 2016;5(3):97-102. doi: 10.11648/j.acm.20160503.11

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  • @article{10.11648/j.acm.20160503.11,
      author = {Liangqiang Zhou and Shanshan Liu and Fangqi Chen},
      title = {Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {3},
      pages = {97-102},
      doi = {10.11648/j.acm.20160503.11},
      url = {https://doi.org/10.11648/j.acm.20160503.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.11},
      abstract = {Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the excitation amplitude to the damping coefficient crosses a critical value, sub-harmonic bifurcations of m order (odd) can occur. The stability conditions of the bifurcation solution for the system parameters are also obtained by using the affection-angle transformation and average method. The result can provide some guidance for the design of this class of sensors.},
     year = {2016}
    }
    

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    T1  - Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor
    AU  - Liangqiang Zhou
    AU  - Shanshan Liu
    AU  - Fangqi Chen
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    DO  - 10.11648/j.acm.20160503.11
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 102
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20160503.11
    AB  - Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the excitation amplitude to the damping coefficient crosses a critical value, sub-harmonic bifurcations of m order (odd) can occur. The stability conditions of the bifurcation solution for the system parameters are also obtained by using the affection-angle transformation and average method. The result can provide some guidance for the design of this class of sensors.
    VL  - 5
    IS  - 3
    ER  - 

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Author Information
  • Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, PR China

  • Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, PR China

  • Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, PR China

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