Journal
CHAOS
Volume 22, Issue 1, Pages -Publisher
AIP Publishing
DOI: 10.1063/1.3678788
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Funding
- Qihang Plan of China University of Mining and Technology (CUMT)
- Scientific Research Foundation for Talents Introduced into CUMT [2011RC13]
- National Natural Science Foundation of China [50975276, 11072107, 91016022]
- Specialized Research Foundation for the Doctoral Program of Higher Education of China [200802900513, 20093218110003]
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The phenomenon of vibrational resonance (VR) is investigated in over-and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single-or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies alpha > 1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is alpha > 1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is alpha < 1. (4) In the underdamped system with single-well potential, there is at most a single-resonance existing for both the cases of ordinary and fractional-order damping. In the underdamped systems, varying the value of the fractional-order is equivalent to change the damping parameter for some cases. (C) 2012 American Institute of Physics. [doi:10.1063/1.3678788]
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