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Research Papers

Energy Harvester Synthesis Via Coupled Linear-Bistable System With Multistable Dynamics

[+] Author and Article Information
Z. Wu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: wuzhen@umich.edu

R. L. Harne, K. W. Wang

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125

1Corresponding author.

Manuscript received February 21, 2013; final manuscript received January 20, 2014; accepted manuscript posted January 27, 2014; published online February 10, 2014. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(6), 061005 (Feb 10, 2014) (9 pages) Paper No: JAM-13-1081; doi: 10.1115/1.4026555 History: Received February 21, 2013; Revised January 20, 2014; Accepted January 27, 2014

In this research we study the dynamics of a coupled linear oscillator-bistable energy harvester system. The method of harmonic balance and perturbation analysis are used to predict the existence and stability of the bistable device interwell vibration. The influences of important parameters on tailoring the coupled system response are investigated to determine strategies for improved energy harvesting performance. We demonstrate analytically that for excitation frequencies in a bandwidth less than the natural frequency of the uncoupled linear oscillator having net mass that is the combination of the bistable and linear bodies, the bistable harvester dynamics may be substantially intensified as compared to a single (individual) bistable harvester. In addition, the linear-bistable coupled system may introduce a stable out-of-phase dynamic around the natural frequency of the uncoupled linear oscillator, enhancing the performance of the harvester by providing a second interwell response not possible when using a single bistable harvester. Key analytical findings are confirmed through numerical simulations and experiments, validating the predicted trends and demonstrating the advantages of the coupled system for energy harvesting.

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Figures

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Fig. 1

Base-excited linear oscillator with attached bistable energy harvester having transduction mechanism and corresponding harvesting circuit

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Fig. 5

High-energy dynamics of the bistable harvester in the coupled system as damping in the linear oscillator γ2 varies

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Fig. 4

High-energy dynamics as electromechanical coupling θ varies. Bistable harvester (a) displacement amplitude (r1); and (b) average power density (P1).

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Fig. 2

High-energy dynamics as mass ratio μ varies. Bistable harvester (a) displacement amplitude (r1); (b) phase lag (ϕ1); and (c) average power density (P1).

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Fig. 3

High-energy dynamics as tuning ratio f varies. Bistable harvester (a) displacement amplitude (r1); and (b) average power density (P1).

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Fig. 9

High-energy dynamics of the bistable harvester in the coupled system as bistable mass varies. (a) Bistable harvester displacement amplitude (r1); and (b) relative acceleration frf of the bistable oscillator inertial mass as a function of bistable mass.

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Fig. 6

High-energy dynamics of the bistable harvester in the undamped coupled system as mass ratio μ changes. Bold curves: stable solutions. Thin lines: unstable solutions. Dashed lines represent the predicted frequency of the in-phase snap-through resonance feature.

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Fig. 7

Photograph of linear-bistable coupled system showing elements of system configuration and test setup

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Fig. 8

Relative acceleration frf of the bistable oscillator inertial mass as a function of damping between linear oscillator and bistable harvester

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