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Research Papers

Experimental Evidence of Vibrational Resonance in a Mechanical Bistable Twin-Well Oscillator

[+] Author and Article Information
Abdrouf Abusoua

Nonlinear Vibrations and Energy Harvesting Lab,
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634

Mohammed F. Daqaq

Engineering Division,
NYU Abu Dhabi,
Saadiyat Campus Experimental Research
Building (C1),
044 P.O. Box 129188,
Abu Dhabi, United Arab Emirates
e-mail: mfd6@nyu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 6, 2017; final manuscript received March 19, 2018; published online April 12, 2018. Assoc. Editor: Massimo Ruzzene.

J. Comput. Nonlinear Dynam 13(6), 061002 (Apr 12, 2018) (6 pages) Paper No: CND-17-1405; doi: 10.1115/1.4039839 History: Received September 06, 2017; Revised March 19, 2018

Vibrational resonance (VR) is a nonlinear phenomenon which occurs when a bistable system is subjected to a biharmonic excitation consisting of a small-amplitude resonant excitation and a large-amplitude high-frequency excitation. The result is that, under some conditions, the high-frequency excitation amplifies the resonant response associated with the slow dynamics. While VR was studied extensively in the open literature, most of the research studies used optical and electrical systems as platforms for experimental investigation. This paper provides experimental evidence that VR can also occur in a mechanical bistable twin-well oscillator and discusses the conditions under which VR is possible. The paper also demonstrates that the injection of the high frequency excitation can be used to change the effective stiffness of the slow response. This can be used for amplification/deamplification of the output signal which can be useful for sensitivity enhancement and/or vibration mitigation.

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Figures

Grahic Jump Location
Fig. 1

Influence of the hard excitation magnitude on the effective potential of the slow dynamics: (a) f̂=0, (b) f̂=100 ms−2, (c) f̂=200 ms−2, (d) f̂=(2/3β3)β1Ω2 ms−2, and (e) f̂=400 ms−2. Results are obtained using Ω=40π rad/s, β1=17 rad/s, and β3=3.8×105 m−2s−2.

Grahic Jump Location
Fig. 2

(a) Schematic and (b) a top view of the experimental setup

Grahic Jump Location
Fig. 3

Frequency response of the slow dynamics for a soft excitation of magnitude (a) g = 0.01 ms−2 and (b) g = 0.2 ms−2. Asterisks represent experimental data and dashed lines represent unstable analytical solutions. Results are obtained using Ω=9.5β1 rads−1, β1=17.28 rads−1, ζ=0.013, and β3=13×105 m−2s−2.

Grahic Jump Location
Fig. 4

Frequency response curve of the bistable system for g = 0.015 ms−2. Results are obtained using Ω=9.5β1 rads−1, β1=17.28 rads−1, ζ=0.013, and β3=13×105 m−2s−2.

Grahic Jump Location
Fig. 5

Frequency response curve of the bistable system for(a)f = 0 ms−2, (b) f = 160 ms−2, (c) f = 320 ms−2, and (d) f = 357 ms−2, g = 0.2 ms−2. Results are obtained using Ω=9.5β1 rads−1, β1=17.28 rads−1, ζ=0.013, and β3=13×105 m−2s−2.

Grahic Jump Location
Fig. 6

Frequency response of the slow dynamics for a softexcitation of magnitude (a) g = 0.01 ms−2 and (b) g = 0.015 ms−2. Circles represent experimental data. Results are obtained using Ω=9.5β1 rads−1, β1=17.28 rads−1, ζ=0.013, and β3=13×105 m−2s−2.

Grahic Jump Location
Fig. 7

Frequency response of (a) the intra- and (b) the interwell dynamics of the system at three different hard excitation levels (f = 0 ms−2, 40 ms−2, 60 ms−2). Dashed lines represent unstable solutions, circles represent a forward experimental sweep, while “x” represents a backward experimental sweep. Results are obtained using g= 0.2 ms−2, Ω=9.5β1 rads−1, β1=17.28 rads−1, ζ=0.013, and β3=13×105 m−2s−2.

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