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Research Papers

Nonlinear Dynamic Characteristics of Variable Inclination Magnetically Coupled Piezoelectric Energy Harvesters

[+] Author and Article Information
Junyi Cao

State Key Laboratory for Manufacturing Systems
Engineering,
Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University,
Xi’an 710049, China;
Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140
e-mail: caojy@mail.xjtu.edu.cn

Shengxi Zhou, Jing Lin

State Key Laboratory for Manufacturing Systems
Engineering,
Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University,
Xi’an 710049, China

Daniel J. Inman

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140
e-mail: daninman@umich.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 3, 2014; final manuscript received November 8, 2014; published online January 20, 2015. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 137(2), 021015 (Apr 01, 2015) (9 pages) Paper No: VIB-14-1203; doi: 10.1115/1.4029076 History: Received June 03, 2014; Revised November 08, 2014; Online January 20, 2015

This paper investigates the nonlinear dynamic characteristics of a magnetically coupled piezoelectric energy harvester under low frequency excitation where the angle of the external magnetic field is adjustable. The nonlinear dynamic equation with the identified nonlinear magnetic force is derived to describe the electromechanical interaction of variable inclination angle harvesters. The effect of excitation amplitude and frequency on dynamic behavior is proposed by using the phase trajectory, power spectrum, and bifurcation diagram. The numerical analysis shows that a rotating magnetically coupled energy harvesting system exhibits rich nonlinear characteristics with the change of external magnet inclination angle. The nonlinear route to and from large amplitude high-energy motion can be clearly observed. It is demonstrated numerically and experimentally that lumped parameters equations with an identified polynomials for magnetic force could adequately describe the characteristics of nonlinear energy harvester. The rotating magnetically coupled energy harvester possesses the usable frequency bandwidth over a wide range of low frequency excitation by adjusting the angular orientation.

Copyright © 2015 by ASME
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References

Figures

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Fig. 1

The nonlinear energy harvester with external magnets of variable inclination

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Fig. 2

Magnetic force curves under different inclination angles

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Fig. 3

Potential energy under different inclination angles

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Fig. 4

Bifurcation diagram of voltage output versus f when θ = 0 deg and A = 0.56 g

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Fig. 5

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 4 Hz

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Fig. 6

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 5 Hz

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Fig. 7

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 9.9 Hz

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Fig. 8

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 13 Hz

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Fig. 9

Bifurcations diagrams for θ = 30 deg, 60 deg, 90 deg, and no magnets

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Fig. 10

Bifurcation diagram of voltage output versus A when θ = 0 deg and f = 10 Hz

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Fig. 11

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.4 g

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Fig. 12

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.45 g

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Fig. 13

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.5 g

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Fig. 14

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.8 g.

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Fig. 15

Experimental setup

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Fig. 16

Increasing frequency sweep experiment for A = 0.56 g

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Fig. 17

Increasing frequency experimental results for f = 8.5 Hz, A = 0.56 g, and θ = 0 deg

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Fig. 18

Different excitation voltage response for θ = 0 deg

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Fig. 19

Constant frequency experimental results for f = 8 Hz, A = 0.56 g, and θ = 0 deg

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Fig. 20

Experimental results for f = 5.2 Hz and A = 0.56 g

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Fig. 21

Experimental results for f = 10 Hz and A = 0.56 g

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Fig. 22

Voltage response under different inclination angles

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Fig. 23

Amplitude sweep voltage responses for θ = 0 deg

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Fig. 24

Amplitude sweep voltage responses for θ = 30 deg

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Fig. 25

Experimental results for f = 10 Hz and A = 0.4 g

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Fig. 26

Experimental results for f = 10 Hz and A = 0.8 g

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Fig. 27

Constant excitation voltage output for θ = 0 deg

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Fig. 28

Constant excitation voltage output for θ = 30 deg

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Fig. 29

Constant excitation voltage output for θ = 60 deg

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