Enhancing the Weak Signal with Arbitrary High-frequency by Vibrational Resonance in Fractional-order Duffing Oscillators

[+] Author and Article Information
J. H. Yang

School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaDepartment of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USAJiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology, Xuzhou 221116, China

Miguel A. F. Sanjuán

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles 28933, Madrid, SpainInstitute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

H. G. Liu

School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China

1Corresponding author.

ASME doi:10.1115/1.4036479 History: Received June 28, 2016; Revised March 05, 2017


When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than one rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In the present work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low-frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional-order and the reduction scale are important factors for the strength of VR.

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