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

Liangqiang Zhou; Shanshan Liu; Fangqi Chen

doi:doi:10.11648/j.acm.20160503.11

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

Liangqiang Zhou, Shanshan Liu, Fangqi Chen

Published in Applied and Computational Mathematics (Volume 5, Issue 3)

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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APA Style

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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TY  - JOUR
T1  - Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor
AU  - Liangqiang Zhou
AU  - Shanshan Liu
AU  - Fangqi Chen
Y1  - 2016/06/08
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.11
DO  - 10.11648/j.acm.20160503.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 97
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

Liangqiang Zhou

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, PR China
Shanshan Liu

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, PR China
Fangqi Chen

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

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APA Style

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor
AU  - Liangqiang Zhou
AU  - Shanshan Liu
AU  - Fangqi Chen
Y1  - 2016/06/08
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.11
DO  - 10.11648/j.acm.20160503.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 97
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  -

Copy | Download