title: Vibrational resonance in Duffing systems with fractional-order damping.
abstract: 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.
authors.affiliation: School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China. jianhuayang@cumt.edu.cn
authors.forename: J H
authors.initials: JH
authors.lastname: Yang
authors.forename: H
authors.initials: H
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D055119:Elastic Modulus; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D014732:Vibration; D014783:Viscosity