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
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