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Title: Triple-well potential with a uniform depth: Advantageous aspects in designing a multi-stable energy harvester
Authors: Kim, Pilkee
Son, Dowung
Seok, Jongwon
Keywords: Bifurcations
Boundary value problems
Issue Date: 2016
Source: Kim, P., Son, D., & Seok, J. (2016). Triple-well potential with a uniform depth: Advantageous aspects in designing a multi-stable energy harvester. Applied Physics Letters, 108(24), 243902-.
Series/Report no.: Applied Physics Letters
Abstract: Analytical expressions for the bi- and tri-stable conditions of a multi-stable energy harvester (MEH) are derived on the basis of bifurcation analyses, and the associated multi-stable regions are characterized in a 2-D parametric space. It is found that a special boundary condition exists for a triple-well with a uniform depth (TU boundary condition), originating from a degenerate pitchfork bifurcation (DPF) point. Interestingly, the outermost well-to-well distance of the triple-well potential, when subjected to the condition that the maximum well depth is kept constant, becomes widest when the well depth is uniform. Accordingly, instead of investigating all possible parametric conditions, the design parameters for the optimal well configuration of the MEH can be sought most efficiently by simply tracing them on the TU boundary. A detailed examination of the potential well configurations along the TU boundary reveals that the most efficient energy harvesting from low-intensity ambient vibrations can be achieved on a TU boundary point, near the DPF point but inevitably a certain distance apart, by inducing an enlarged interwell motion. This investigation is experimentally validated.
ISSN: 0003-6951
DOI: 10.1063/1.4954169
Schools: School of Mechanical and Aerospace Engineering 
Rights: © 2016 American Institute of Physics. This paper was published in Applied Physics Letters and is made available as an electronic reprint (preprint) with permission of American Institute of Physics. The published version is available at: []. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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