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Research Papers

Harvesting Energy From Time-Limited Harmonic Vibrations: Mechanical Considerations

[+] Author and Article Information
M. J. Brennan

Departamento de Engenharia Mecânica,
UNESP,
Ilha Solteira 15385-000, São Paulo, Brazil
e-mail: mjbrennan0@btinternet.com

G. Gatti

Department of Mechanical,
Energy and Management Engineering,
University of Calabria,
Arcavacata di Rende, CS 87036, Italy
e-mail: gianluca.gatti@unical.it

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 30, 2016; final manuscript received April 29, 2017; published online July 26, 2017. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 139(5), 051019 (Jul 26, 2017) (6 pages) Paper No: VIB-16-1329; doi: 10.1115/1.4036867 History: Received June 30, 2016; Revised April 29, 2017

Single-degree-of-freedom (SDOF) mechanical oscillators have been the most common type of generators used to harvest energy from mechanical vibrations. When the excitation is harmonic, optimal performance is achieved when the device is tuned so that its natural frequency coincides with the excitation frequency. In such a situation, the harvested energy is inversely proportional to the damping in the system, which is sought to be very low. However, very low damping means that there is a relatively long transient in the harvester response, both at the beginning and at the end of the excitation, which can have a considerable effect on the harvesting performance. This paper presents an investigation into the mechanical design of a linear resonant harvester to scavenge energy from time-limited harmonic excitations to determine an upper bound on the energy that can be harvested. It is shown that when the product of the number of excitation cycles and the harvester damping ratio is greater (less) than about 0.19, then more (less) energy can be harvested from the forced phase of vibration than from the free phase of vibration at the end of the period of excitation. The analytical expressions developed are validated numerically on a simple example and on a more practical example involving the harvesting of energy from trackside vibrations due to the passage of a train.

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Figures

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Fig. 1

Energy harvester subject to time-limited harmonic base excitation: (a) mechanical components of the energy harvester in which it assumed that the energy dissipated by the damper is the same as the energy harvested and (b) time history of the base input and the response of the harvester mass

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Fig. 2

Characteristics of the energy harvester subject to time-limited harmonic excitation: (a) nondimensional energy harvested: during the excitation phase (dotted line), after the excitation phase (solid line), and total (dashed line), (b) ratio of energy harvested during forced and free vibration to the total energy harvested: during the excitation phase (dotted line) and after the excitation phase (solid line), and (c) maximum nondimensional relative displacement. The circle corresponds to the case when the energy harvested during the excitation phase is a maximum. The square corresponds to the case when the energy harvested during forced and free vibration is equal.

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Fig. 3

Design parameters for the energy harvester. The damping ratio ζ is shown as a function of n for various values of πnζ. The shaded (nonshaded) part of the figure corresponds to the case when the energy harvested during free vibration is greater (less) than that harvested during forced vibration.

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Fig. 4

Nondimensional time histories for time-limited harmonic excitation: (a) relative displacement for πnζ=0.1, (b) relative displacement for πnζ=1, (c) relative displacement for πnζ=10, and (d) base displacement

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Fig. 5

Measured vertical acceleration of a sleeper as an Intercity 125 train passes by, as in Ref. [15]: (a) time history and (b) normalized power spectral density as a function of trainload frequency (frequency×carriage length (L)/train velocity (V) )

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Fig. 6

Time histories of the energy harvester for time-limited harmonic excitation due to the passing of a train: (a) relative displacement for πnζ=0.1, (b) relative displacement for πnζ=1, (c) relative displacement for πnζ=10, and (d) acceleration of the base

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