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Research Papers

Internal Resonance Energy Harvesting

[+] Author and Article Information
Li-Qun Chen

Department of Mechanics,
Shanghai University,
Shanghai 200444, China
Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: lqchen@staff.shu.edu.cn

Wen-An Jiang

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: anan0397@163.com

1Corresponding author.

Manuscript received August 16, 2014; final manuscript received January 12, 2015; published online January 29, 2015. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 82(3), 031004 (Mar 01, 2015) (11 pages) Paper No: JAM-14-1373; doi: 10.1115/1.4029606 History: Received August 16, 2014; Revised January 12, 2015; Online January 29, 2015

Internal resonance is explored as a possible mechanism to enhance vibration-based energy harvesting. An electromagnetic device with snap-through nonlinearity is proposed as an archetype of an internal resonance energy harvester. Based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude–frequency response relationships of the displacement and the power in the first primary resonances with the two-to-one internal resonance. The amplitude–frequency response curves have two peaks bending to the left and the right, respectively. The numerical simulations support the analytical results. Then the averaged power is calculated under the Gaussian white noise, the narrow-band noise, the colored noise defined by a second-order filter, and the exponentially correlated noise. The results demonstrate numerically that the internal resonance design produces more power than other designs under the Gaussian white noise and the exponentially correlated noise. Besides, the internal resonance energy harvester can outperform the linear energy harvesters with the same natural frequencies and in the same size under Gaussian white noise.

Copyright © 2015 by ASME
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Figures

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Fig. 1

Schematics of a snap-through electromagnetic energy harvester with an additional oscillator

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Fig. 2

Amplitude–frequency response curves for different excitation amplitudes. (a) Displacements and (b) power.

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Fig. 3

Amplitude–frequency response curves for different damping coefficients. (a) Displacements for varying c1, (b) power for varying c1, (c) displacements for varying c2, and (d) power for varying c2.

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Fig. 11

Comparisons of nonlinear and linear energy harvesters

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Fig. 13

The averaged power versus the intensity of narrow-band colored noise

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Fig. 5

Amplitude–frequency response curves for different magnetic flux densities. (a) Displacements and (b) power.

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Fig. 6

Amplitude–frequency response curves for different coil length levels. (a) Displacements and (b) power.

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Fig. 7

Comparisons of analytical and numerical results. (a) Displacements and (b) power.

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Fig. 8

Schematics of two linear electromagnetic energy harvesters

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Fig. 4

Amplitude–frequency response curves for different resistances. (a) Displacements and (b) power.

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Fig. 9

Amplitude–frequency response curves of nonlinear and linear energy harvesters

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Fig. 10

The averaged power versus Gaussian white noise excitation intensity

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Fig.12

The averaged power versus the center frequency of a narrow-band colored noise

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Fig. 16

The averaged power versus the intensity of exponentially correlated noise

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Fig. 17

The averaged power versus the bandwidth of exponentially correlated noise

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Fig. 14

The averaged power versus the center frequency of colored noise

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Fig. 15

The averaged power versus the intensity of colored noise

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