Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 18, Issue 5, Pages 1316-1326Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2012.09.023
Keywords
Vibrational resonance; Fractional-order damping; Time delay feedback
Categories
Funding
- Fundamental Research Funds for the Central Universities [2012QNA21]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
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We develop an analytical technique to investigate the phenomenon of vibrational resonance in a fractional-order Duffing system with linear time delay feedback and driven by both low frequency and high frequency periodic signals. At first, the theoretical predication of the response amplitude at the low-frequency is obtained by the method of direct separation of slow and fast motions. Then, the bifurcation analysis is carried out based on three kinds of resonance behaviors. Further, influences of the high frequency signal, the fractional-order damping and the delay parameter on the vibrational resonance are discussed by both theoretical and numerical simulations. If the value of the fractional-order is a controllable parameter, the monotonicity of the response amplitude versus the value of the fractional-order depends on the amplitude of the high-frequency signal. If the delay parameter is a controllable parameter, the response amplitude with respect to the delay parameter presents periodic or quasi-periodic pattern, and it is similar to that in the integer-order differential system with linear time delay feedback. The good agreement between the analytical and numerical results indicates the validity of the theoretical predications. (C) 2012 Elsevier B.V. All rights reserved.
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