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Review Article

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

[+] Author and Article Information
Mohammed F. Daqaq

Associate Professor
Nonlinear Vibrations and Energy
Harvesting Lab (NOVEHL),
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: mdaqaq@clemson.edu

Ravindra Masana

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: rmasana@g.clemson.edu

Alper Erturk

Assistant Professor
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332–0405
e-mail: alper.erturk@me.gatech.edu

D. Dane Quinn

Professor
Department of Mechanical Engineering,
The University of Akron,
Akron, OH 44325–3903
e-mail: quinn@uakron.edu

In addition to the primary resonant excitations, nonlinear systems can exhibit secondary resonances at fraction or multiple integers of the natural frequency.

1Corresponding author.

Manuscript received March 25, 2013; final manuscript received October 16, 2013; published online May 2, 2014. Assoc. Editor: Chin An Tan.

Appl. Mech. Rev 66(4), 040801 (May 02, 2014) (23 pages) Paper No: AMR-13-1019; doi: 10.1115/1.4026278 History: Received March 25, 2013; Revised October 16, 2013

The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature's attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting.

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References

Figures

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Fig. 1

Schematic of a linear cantilevered piezoelectric energy harvester and its steady-state voltage response curve. Here, ab(t) refers to the base acceleration, Ω is the excitation frequency, and ωn is the first modal frequency of the beam.

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Fig. 2

(a) Schematic of a nonlinear cantilevered piezoelectric energy harvester. (b) Variation of the restoring force due to the nonlinearity.

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Fig. 3

A simplified representation of a generic vibratory energy harvester

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Fig. 4

Restoring force and energy potentials of different nonlinear vibratory energy harvesters

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Fig. 5

The dynamics of a nonlinear energy harvester can be fairly well understood via a simple analogy with a particle moving along a cart. (a) Monostable potential and (b) bistable potential.

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Fig. 6

Frequency response of the particle in the monostable potential

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Fig. 7

Basins of attraction of the multiple solutions of a monostable system

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Fig. 8

Frequency response of the particle in a monostable potential for a path with softening nonlinearity. (a) Changing the forcing amplitude, A, and (b) changing the damping ratio, ζ.

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Fig. 9

(a) Potential energy; (b) intrawell oscillations

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Fig. 10

Frequency response of the particle in a single potential well of the bistable potential system when A<A1. Dashed lines represent unstable periodic responses.

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Fig. 11

Frequency response of the particle in a single potential well of the bistable potential system when A1<A<A2. Dashed lines represent unstable periodic responses.

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Fig. 12

Basins of attraction of the multiple solutions of a bistable system for an intermediate value of the input excitation A1<A<A2. (a) Basins of attraction for a frequency ratio slightly higher than the period doubling pd bifurcation. (b) Basins of attraction for a frequency ratio within the chaotic region, CH. Here, B'r and B'n are the attractors of the opposite well.

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Fig. 13

Bifurcation diagram for the bistable potential system when A > A2. Here, BL represents the large-orbit branch of interwell oscillations; Bn and B'n represent nonresonant intrawell oscillations within the two opposing wells; Br and B'r represent resonant intrawell oscillations within the two opposing wells; cri represents boundary crises; pd is a period-doubling bifurcation; nT represents periodic solutions having n× the period of excitation, and CH represents chaotic solutions.

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Fig. 14

Cartoon schematics of monostable energy harvester. (a) Inductive energy harvester proposed by Burrow and Clare [46], (b) inductive energy harvester proposed by Mann and Sims [29], (c) piezoelectric energy harvester proposed by Stanton et al. [48] and Sebald et al. [49], and (d) piezoelectric energy harvester proposed by Masana and Daqaq [32].

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Fig. 15

Examples of capacitive monostable VEHs fabricated for MEMS applications. Part (a) is adapted from “Large-amplitude MEMS Electret Generator with Nonlinear Springs,” by Miki et al., 2010, published in 2010 IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS). Reproduced by permission of IEEE Publishing. All rights reserved. Part (b) is adapted from “Fabrication and Characterization of a Wideband MEMS Energy Harvester Utilizing Nonlinear Springs,” by Nguyen et al., 2010, Journal of Micromechanics and Microengineering, 20. Reproduced by permission of IOP Publishing. All rights reserved.

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Fig. 16

(a) Influence of the backward coupling κ on the steady-state frequency response of the mechanical subsystem near a primary resonant excitation. (b) Power response of a capacitive-type monostable VEH with δ=-200, ζ=0.005, A=0.001, Cp=1×10-7F, k1=1000N/m, α=1, and different values of κ. Dashed lines represent unstable periodic responses.

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Fig. 17

Variation of the electric damping ζe with the time constant ratio, α

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Fig. 18

Frequency and power response of a capacitive-type monostable harvester with δ=200, ζ=0.005, A=0.001, Cp=1×10-7F, k1=1000N/m, θ=0.002N/Volt

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Fig. 19

Power response of a capacitive-type monostable harvester with κ2=0.25, ζ=0.01, A=0.001, Cp=1×10-7F, k1=1000N/m, and α=1

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Fig. 20

A schematic of parametrically exited energy harvesters considered by (a) Daqaq et al. [65] and (b) Ma et al. [67]

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Fig. 21

Schematics of the bistable piezoelectric energy harvester configurations suggested by (a) Erturk et al. [76], (b) Cottone et al. [75], and (c) Masana and Daqaq [86]

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Fig. 22

Experimental voltage versus velocity trajectories of bistable (piezomagnetoelastic) and monostable (piezoelastic) energy harvesters showing the advantage of the high-energy (interwell) orbits in the bistable harvester, which may coexist with (a) chaotic and (b) low-energy (intrawell) periodic attractors; (c) power frequency response curves of bistable and monostable energy harvesters for the same excitation level [76,93]

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Fig. 23

Numerical frequency-response curves of the bistable energy harvester proposed by Masana and Daqaq [78]. (a) A bistable potential with deep wells. (b) A bistable potential with shallow wells. Dots represent a bifurcation map and solid regions represent the amplitude of the steady-state time history.

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Fig. 24

Voltage frequency response of a bistable axially loaded VEH near its primary resonance. BL represents large-orbit branch interwell oscillations, Bn represents nonresonant intrawell oscillations, Br represents resonant interwell oscillations, cri represents a boundary crisis, pd is a period-doubling bifurcation, nT represents solutions having n× the period of excitation, and CH represents chaotic solutions. Results are obtained for Eq. (4) with ζ=0.05, r=1.5, δ=0.5, κ2=0.01, α=0.1, and a base excitation A=0.175.

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Fig. 25

Open-circuit voltage frequency response curves for a bistable harvester at three different excitation levels. Results are obtained for Eq. (4) with ζ=0.05, r=1.5, δ=0.5, and a base excitation of normalized amplitude (a) A = 0.08, (b) A=0.1, and (c) A=0.175.

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Fig. 26

(a) Restoring force magnitude of the piecewise linear electromagnetic harvester with one-sided stopper studied by Soliman et al. [104], and (b) its voltage-frequency response exhibiting bandwidth enhancement in an increasing frequency sweep. Adapted from “A Wideband Vibration-based Energy Harvester,” by Soliman et al., 2008, Journal of Micromechanics and Microengineering, 18. Reproduced by permission of IOP Publishing. All rights reserved.

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Fig. 27

(a) Voltage and (b) power frequency response curves obtained via bidirectional frequency sweeps in two MEMS electrostatic energy harvesters with two-sided stoppers as reported by (a) Hoffmann et al. [106] and (b) Le et al. [107]. Part (a) is adapted from “Fabrication, Characterization and Modeling of Electro-static Micro-generators,” by Hoffmann et al., 2009, Journal of Micromechanics and Microengineering, 19. Reproduced by permission of IOP Publishing. All rights reserved. Part (b) is adapted from “Microscale Electrostatic Energy Harvester Using Internal Impacts,” by Le et al., 2012, Journal of Intelligent Material Systems and Structures, 23. Reproduced by permission of SAGE Publishing. All rights reserved.

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Fig. 28

Voltage-frequency response curves of a bistable VEH operating near half its fundamental frequency as reported by Masana and Daqaq [86]. (a) Theoretical and (b) experimental results.

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