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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013112 (2012); http://dx.doi.org/10.1063/1.3678788 (9 pages)

Vibrational resonance in Duffing systems with fractional-order damping

J. H. Yang and H. Zhu

School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China

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(Received 12 September 2011; accepted 1 January 2012; published online 27 January 2012)

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 α > 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 α > 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 α < 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.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. OVERDAMPED FRACTIONAL-ORDER DUFFING SYSTEM
    1. Theoretical analysis for the response amplitude
    2. The double-well case
    3. The single-well case
  3. UNDERDAMPED FRACTIONAL-ORDER DUFFING SYSTEM
    1. Theoretical analysis for the response amplitude
    2. The double-well case
    3. The single-well case
  4. CONCLUSIONS

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KEYWORDS and PACS

Keywords

damping, nonlinear dynamical systems

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3678788

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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