Research Papers

A Broadband Internally Resonant Vibratory Energy Harvester

[+] Author and Article Information
Li-Qun Chen

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

Wen-An Jiang

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China

Meghashyam Panyam

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

Mohammed F. Daqaq

Nonlinear Vibrations and Energy Harvesting Laboratory,
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: mdaqaq@clemson.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 30, 2015; final manuscript received July 13, 2016; published online August 16, 2016. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 138(6), 061007 (Aug 16, 2016) (10 pages) Paper No: VIB-15-1412; doi: 10.1115/1.4034253 History: Received September 30, 2015; Revised July 13, 2016

The objective of this paper is twofold: first to illustrate that nonlinear modal interactions, namely, a two-to-one internal resonance energy pump, can be exploited to improve the steady-state bandwidth of vibratory energy harvesters; and, second, to investigate the influence of key system’s parameters on the steady-state bandwidth in the presence of the internal resonance. To achieve this objective, an L-shaped piezoelectric cantilevered harvester augmented with frequency tuning magnets is considered. The distance between the magnets is adjusted such that the second modal frequency of the structure is nearly twice its first modal frequency. This facilitates a nonlinear energy exchange between these two commensurate modes resulting in large-amplitude responses over a wider range of frequencies. The harvester is then subjected to a harmonic excitation with a frequency close to the first modal frequency, and the voltage–frequency response curves are generated. Results clearly illustrate an improved bandwidth and output voltage over a case which does not involve an internal resonance. A nonlinear model of the harvester is developed and validated against experimental findings. An approximate analytical solution of the model is obtained using perturbation methods and utilized to draw several conclusions regarding the influence of key design parameters on the harvester’s bandwidth.

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Grahic Jump Location
Fig. 1

A schematic diagram of the L-shaped internally resonant VEH

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Fig. 2

Setup used in the experiments

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Fig. 3

The first two flexural normal modes of the internally resonant VEH: (a) mode 1 and (b) mode 2

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Fig. 4

Variation of the output voltage with the excitation frequency and a base acceleration of 0.5 m/s2. The results are obtained for a load resistance of 25 kΩ.

Grahic Jump Location
Fig. 5

Variation of the output voltage with the excitation frequency in the vicinity of the first modal frequency. (a) Linear response in the absence of the magnetic field, (b) nonlinear response in the presence of the magnetic field but away from the internal resonance, (c) internally resonant response, and (d) comparison between the internally and noninternally resonant responses for f1=0.0025. The results are obtained using R = 25 kΩ, a modal damping ratios of ζ1=0.005 and ζ2=0.005, and base accelerations of 0.5 m/s2 and 1 m/s2 for the internally resonant case. Dotted lines represent unstable fixed points of the modulation equations. Markers represent experimental data obtained using the setup shown in Fig. 2.

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Fig. 8

Coordinate system used in the derivation

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Fig. 6

Variation of the output voltage with the excitation frequency in the vicinity of the first modal frequency. (a) Different first-modal damping ratios, second modal damping ratio of ζ2=0.005, and an acceleration level of 0.5 m/s2. (b) Different base acceleration levels 0.5,1, and 1.5 m/s2 and damping ratios of ζ1,2=0.005. The results are obtained using R = 25 kΩ, and dotted lines represent unstable fixed points of the modulation equations.

Grahic Jump Location
Fig. 7

Variation of the output power with the excitation frequency in the vicinity of the first modal frequency. (a) Different load resistances. (b) Different first-modal couplings and R = 25 kΩ. The results are obtained for a base acceleration of 1 m/s2, and modal damping ratios of ζ1,2=0.005. Dotted lines represent unstable fixed points of the modulation equations.



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