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Research Papers

Influence of Piezoelectric Energy Transfer on the Interwell Oscillations of Multistable Vibration Energy Harvesters

[+] Author and Article Information
Aravind Kumar

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: aravindkumark@outlook.com

Shaikh Faruque Ali

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: sfali@iitm.ac.in

A. Arockiarajan

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: aarajan@iitm.ac.in

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 12, 2018; final manuscript received November 22, 2018; published online January 11, 2019. Assoc. Editor: Massimo Ruzzene.

J. Comput. Nonlinear Dynam 14(3), 031001 (Jan 11, 2019) (11 pages) Paper No: CND-18-1015; doi: 10.1115/1.4042139 History: Received January 12, 2018; Revised November 22, 2018

This manuscript investigates the effect of nonconservative electromechanical energy transfer on the onset of interwell motions in multistable piezoelectric energy harvesters. Multistable piezoelectric energy harvesters have been proven to outperform their linear counterparts when they undergo interwell oscillations. The conditions for interwell oscillations in such harvesters are generally characterized in terms of their potential energy function. This is accurate for a stand-alone mechanical oscillator but when the piezoelectric patches and a load resistance are included, a part of the kinetic energy supplied to the system is converted into electrical energy. In this manuscript, the Melnikov necessary conditions for interwell oscillations are derived, considering the effect of this nonconservative piezoelectric energy transfer. Through Melnikov theoretic analysis, it is shown that in a tristable harvester with all the three potential wells having the same depth, a higher excitation level is required to enable exits from the middle well to the outer wells when compared to the exits from the outer wells to the middle well. This is in stark contrast to a stand-alone tristable mechanical oscillator wherein interwell motions are simultaneously enabled for all the wells having the same depth.

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Figures

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Fig. 1

Schematic representation of a magneto-elastically buckled energy harvester employing two external magnets

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Fig. 2

Phase portraits indicating the homoclinic and heteroclinic orbits corresponding to the conservative system of (a) bistable configuration and (b) tristable configuration

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Fig. 3

Variation in the homoclinic Melnikov scale factor Sh(ω) with respect to ω for the bistable harvester

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Fig. 4

Variation in the electromechanical dissipation factor ψh with respect to λ for the bistable harvester

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Fig. 5

Variation in the homoclinic critical excitation Fh with respect to ω for the stand-alone mechanical oscillator and the bistable harvester for different decay fractions

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Fig. 6

Potential energy function corresponding to the tristable configuration having potential wells of equal depth. The homoclinic and heteroclinic orbits are also shown in the figure.

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Fig. 7

Variation in the homoclinic and heteroclinic Melnikov scale factors with respect to the excitation frequency for the tristable harvester

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Fig. 8

Variation in the homoclinic and heteroclinic Melnikov critical amplitudes with respect to the excitation frequency for the tristable harvester. The highlighted region represents the range of excitation amplitudes and frequencies for which theharvester can undergo interwell motions encompassing all the three wells.

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Fig. 9

Variation in the homoclinic and heteroclinic electromechanical dissipation factors with respect to λ for the tristable harvester

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Fig. 10

Variation in the homoclinic critical excitation with respect to ω for different values of λ for the tristable harvester

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Fig. 11

Variation in the heteroclinic critical excitation with respect to ω for different values of λ for the tristable harvester

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Fig. 12

Effect of the linear stiffness coefficient k1 on the homoclinic critical excitation Fh for the bistable harvester

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Fig. 13

Effect of the cubic stiffness coefficient k2 on the homoclinic critical excitation Fh for the bistable harvester

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Fig. 14

Effect of the linear stiffness coefficient k1 on the homoclinic (left) and the heteroclinic (right) critical excitations for the tristable harvester

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Fig. 15

Effect of the cubic stiffness coefficient k2 on the homoclinic (left) and the heteroclinic (right) critical excitations for the tristable harvester

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Fig. 16

Effect of the quintic stiffness coefficient k3 on the homoclinic (left) and the heteroclinic (right) critical excitations for the tristable harvester

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