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Research Papers

Complexification-Averaging Analysis on a Giant Magnetostrictive Harvester Integrated With a Nonlinear Energy Sink

[+] Author and Article Information
Zhi-Wei Fang

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

Ye-Wei Zhang

Faculty of Aerospace Engineering,
Shenyang Aerospace University,
Shenyang 110136, China
e-mail: zhangyewei1218@126.com

Xiang Li

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: xiangli9@163.com

Hu Ding

Shanghai Key Laboratory of
Mechanics in Energy Engineering,
Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: dinghu3@shu.edu.cn

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

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 22, 2017; final manuscript received September 7, 2017; published online October 12, 2017. Assoc. Editor: Alper Erturk.

J. Vib. Acoust 140(2), 021009 (Oct 12, 2017) Paper No: VIB-17-1276; doi: 10.1115/1.4038033 History: Received June 22, 2017; Revised September 07, 2017

The present study aims to investigate the steady-state response regimes of a device comprising a nonlinear energy sink (NES) and a giant magnetostrictive energy harvester utilizing analytical approximation. The complexification-averaging (CX-A) technique is generalized to systems defined by differential algebraic equations (DAEs). The amplitude-frequency responses are compared with numerical simulations for validation purposes. The tensile and compressive stresses of giant magnetostrictive material (GMM) are checked to ensure that the material functions properly. The energy harvested is calculated and the comparison of transmissibility of the apparatus with and without NES–GMM is exhibited to reveal the performance of vibration mitigation. Then, the stability and bifurcations are examined. The outcome demonstrates that the steady-state periodic solutions of the system undergo saddle-node (SN) bifurcation at a certain set of parameters. In the meantime, no Hopf bifurcation is observed. The introduction of NES and GMM for vibration reduction and energy harvesting brings about geometric nonlinearity and material nonlinearity. By computing both the responses of the primary system equipped with the NES only and the NES–GMM, it is indicated that the added GMM can dramatically modify the steady-state dynamics. A further optimization with respect to the cubic stiffness, the damper of NES, and the amplitude of excitation is conducted, respectively. The boundary where the giant magnetostrictive energy harvester is out of work is pointed out as well during the process of optimizing.

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References

Figures

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Fig. 1

The amplitude-frequency response curves for the first set of parameters

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Fig. 2

The amplitude-frequency response curves for the second set of parameters

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Fig. 3

The maximum and minimum stress of GMM for the second set of parameters

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Fig. 4

Comparison of the transmissibility of displacement in a system with NES–GMM and without NES–GMM for the second set of parameters

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Fig. 5

The maximum voltage (a) and the maximum power (b) obtained for the second set of parameters

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Fig. 6

Curves of SN bifurcations for the second set of parameters: (a) f = 32 Hz and (b) distinct frequencies

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Fig. 7

Surfaces of the SN bifurcations for the second set of parameters: (a) top view and (b) bottom view

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Fig. 8

The amplitude-frequency response curves with GMM and without GMM for the second set of parameters

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Fig. 9

The amplitude-frequency response curves (a) and the enlargement (b) when the cubic stiffness of NES varies

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Fig. 10

The maximum and minimum stress of the GMM (a) and the enlargement (b) when the cubic stiffness of NES varies

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Fig. 11

The transmissibility of displacement (a) and the enlargement (b) when the cubic stiffness of NES varies

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Fig. 12

The maximum voltage (a) and the enlargement (b) when the cubic stiffness of NES varies

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Fig. 13

The maximum power (a) and the enlargement (b) when the cubic stiffness of NES varies

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Fig. 14

The amplitude-frequency response curves when the amplitude of excitation varies

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Fig. 15

The maximum and minimum stress of the GMM (a) and the enlargement (b) when the amplitude of excitation varies

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Fig. 16

The transmissibility of displacement (a) and the enlargement (b) when the amplitude of excitation varies

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Fig. 17

The maximum voltage when the amplitude of excitation varies

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Fig. 18

The maximum power (a) and the enlargement (b) when the amplitude of excitation varies

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Fig. 19

The amplitude-frequency response curves when the damper of NES varies

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Fig. 20

The maximum and minimum stress of the GMM (a) and the enlargement (b) when the damper of NES varies

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Fig. 21

The transmissibility of displacement when the damper of NES varies

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Fig. 22

The maximum voltage (a) and the enlargement (b) when the damper of NES varies

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Fig. 23

The maximum power (a) and the enlargement (b) when the damper of NES varies

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