Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 97-102
Received: Jun. 7, 2016; Published: Jun. 8, 2016
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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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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.
Sub-harmonic Bifurcation, Carbon Nanotube, Sub-harmonic Melnikov Method, Stability
To cite this article
Liangqiang Zhou, Shanshan Liu, Fangqi Chen, Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 97-102. doi: 10.11648/j.acm.20160503.11
S. Iijima, Helical microtubules of graphitic carbon. Nature 354(6348), 56–58 (1991).
S. J. Tans, A. R. M. Verschueren, C Dekker, Roomtemperature transistor based on a single carbon nanotube. Nature 393(6680), 49–52 (1998).
R. Martel, T. Schmidt, H. R. Shea, T. Hertel, P. Avouris, Single- and multi-wall carbon nanotube field-effect transistors. Appl. Phys. Lett. 73(17), 2447–2449 (1998).
W. A. De Heer, W. S. Bacsa, A. Châtelain, T. Gerfin, R. Humphrey-Baker, L. F orro, D. Ugarte, Aligned carbon nanotube films: production and optical and electronic properties. Science 268(5212), 845–847 (1995).
A. Zettl, xtreme oxygen sensitivity of electronic properties of carbon nanotubes. Science 287(5459), 1801–1804 (2000).
J. Kong, N. R. Franklin, C. Zhou, M. G. Chapline, S. Peng, K. Cho, H Dai, Nanotube molecular wires as chemical sensors. Science 287(5453), 622–625 (2000).
G. Che, B. B. Lakshmi, E. R. Fisher, C. R. Martin. Carbon nanotubule membranes for electrochemical energy storage and production. Nature 393(6683), 346–349 (1998).
R. F. Gibson, O. A. Emmanuel, F. W. Yuan. Vibrations of carbon nanotubes and their composites: a review. Compos Sci Technol 2007; 67(1): 1–28.
D, Qian. E. C. Dickey. R. Andrews, T. Rantell. Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites. Appl Phys Lett 2000; 76(20): 2868–70.
Z. L. Wang. P. Poncharal. W. A. Heer. Nanomeasurements of individual carbon nanotubes by in situ TEM. Pure Appl Chem 2000; 72(1–2): 209–19.
X. Guo, A. Y. T. Leung, X. Q. He, et al. Bending buckling of single-walled carbon nanotubes by atomic-scale finite element, Composites: Part B Engineering, 2008; 39(1): 202-208.
C. Wang, J. C. Cao, Terahertz generation and chaotic dynamics in single-walled zigzag carbon nanotubes, Chaos, 2009; 19: 033136.
A. Y. Joshi, S. C. Sharma, S. P. Harma, Nonlinear dynamic analysis of single-walled carbon nanotube based mass sensor, Journal of Nanotechnology in Engineering and Medicine, 2011; 2: 041008.
A. Y. Joshi, S. C. Sharma, S. P. Harsha, Chaotic responses analysis of single-walled carbon nanotube due to surface deviations, NANO: Brief Reports and Reviews, 2012; 7(2): 1250008.
W. P. Hu, Z. C. Deng, B. Wang. et al. Chaos in an embedded single-walled carbon nanotube, Nonlinear Dynamics, 2013; 73(1): 389-398.
Y. L. Kuo, Chaotic Analysis of the Geometrically Nonlinear Nonlocal Elastic Single-Walled Carbon Nanotubes on Elastic Medium, Journal of Nanoscience and Nanotechnology, 2014, 14(3): 2352-2360.
J. S. Fang, Chaotic behavior and its control in the single-wall carbon nanotube, International Journal of Modern Physics B, 2014, 28: 1450005.
I. K. Kim, S. I. Lee, Nonlinear resonances of a single-wall carbon nanotube cantilever, Physica E, 2015, 67: 159-167.
W. P. Hu, Z. C. Deng, Chaos in embedded fluid-conveying single-walled carbon nanotube under transverse harmonic load series, Nonlinear Dynamics, 2015, 79(1): 325-333.
M. M. S. Fakhrabadi, Prediction of small-scale effects on nonlinear dynamic behaviors of carbon nanotube-based nano-resonators using consistent couple stress theory, Composites Part B, 2016, 88(1): 26-35.
J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcaions of Vector Fields, Springer, New York, 1997, pp. 195.
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