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Research Papers

Prospects for Nonlinear Energy Harvesting Systems Designed Near the Elastic Stability Limit When Driven by Colored Noise

[+] Author and Article Information
R. L. Harne

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

K. W. Wang

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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 27, 2013; final manuscript received November 26, 2013; published online December 24, 2013. Assoc. Editor: Brian P. Mann.

J. Vib. Acoust 136(2), 021009 (Dec 24, 2013) (8 pages) Paper No: VIB-13-1181; doi: 10.1115/1.4026212 History: Received May 27, 2013; Revised November 26, 2013

Ambient vibration sources in many prime energy harvesting applications are characterized as having stochastic response with spectra concentrated at low frequencies and steadily reduced power density as frequency increases (colored noise). To overcome challenges in designing linear resonant systems for such inputs, nonlinear restoring potential shaping has become a popular means of extending a harvester's bandwidth downward towards the highest concentration of excitation energy available. Due to recent works which have individually probed by analysis, simulation, or experiment the opportunity for harvester restoring potential shaping near the elastic stability limit (buckling transition) to improve power generation in stochastic environments—in most cases focusing on postbuckled designs and in some cases arriving at conflicting conclusions—we seek to provide a consolidated and insightful investigation for energy harvester performance employing designs in this critical regime. Practical aspects drive the study and encourage evaluation of the role of asymmetries in restoring potential forms. New analytical, numerical, and experimental investigations are conducted and compared to rigorously assess the opportunities and reach well-informed conclusions. Weakly bistable systems are shown to potentially provide minor performance benefits but necessitate a priori knowledge of the excitation environment and careful avoidance of asymmetries. It is found that a system designed as close to the elastic stability limit as possible, without passing the buckling transition, may be the wiser solution to energy harvesting in colored noise environments.

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Figures

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Fig. 3

Measured natural frequencies of beam as equal magnet spacing d is adjusted. Inset shows test schematic

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Fig. 2

Cantilevered ferromagnetic beam with PVDF patch and adjustable attractive magnets, attached to electrodynamic shaker

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Fig. 1

Nonlinear energy harvester with piezoelectric and electromagnetic induction mechanisms and corresponding circuitry

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Fig. 4

Beam velocity ring-down response for case of magnet spacing d = 15 mm, near point of essential nonlinearity

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Fig. 5

Harvester mean-square velocity normalized to noise correlation maxima. Row (a) and (b) analytical results and simulated data (filled-in marks). Row (c) and (d) experimental results with legends indicating mean-square noise input acceleration values.

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Fig. 6

Influence of linear stiffness term κ on harvester mean-square velocity normalized to excitation level

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Fig. 7

Influence of bias α on harvester mean-square velocity normalized to excitation level. (a) Analysis; (b) experimental setup for evaluating influence of gravitational bias; and (c)–(e) experimental harvester mean-square voltage responses normalized to data for inclination θ = 0 using increasing noise excitation levels from (c) to (e). Legends indicate mean-square base acceleration levels for each test.

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