Journal
NONLINEAR DYNAMICS
Volume 89, Issue 4, Pages 2621-2628Publisher
SPRINGER
DOI: 10.1007/s11071-017-3610-2
Keywords
Weak high-frequency character signal; Scale transformation; Vibrational resonance
Categories
Funding
- Fundamental Research Funds for the Central Universities [2015XKMS023]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
- Top-notch Academic Programs Project of Jiangsu Higher Education Institutions
- Spanish Ministry of Economy and Competitiveness [FIS2013-40653-P]
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The weak high-frequency character signal (HCS) cannot be detected substantially by the traditional vibrational resonance (VR) theory. In this paper, by introducing the scale transformation, the HCS in the original system can be transformed to the low-frequency character signal in the rescaled system. As we know, the two systems are equivalent and the VR can occur at low frequency in the rescaled system. Then, the VR can also occur at high frequency in the original system. We take the underdamped bistable system and the overdamped bistable system of the Duffing oscillator as examples. The method proposed in this paper is verified by both theoretical analysis and numerical simulations. The results obtained by the two ways are in good agreement. The results in this paper provide a tool to detect the weak character signal with arbitrary frequency in the engineering problems.
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