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Journal of Vibration and Acoustics | Volume 139 | Issue 5 | research-article
Research Papers

Dynamics of Transition Regime in Bistable Vibration Energy Harvesters

[+] Author and Article Information
Alwathiqbellah Ibrahim

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902
e-mail: aibrahi4@binghamton.edu

Shahrzad Towfighian

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902
e-mail: stowfigh@binghamton.edu

Mohammad I. Younis

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902;
Physical Science and Engineering Division,
King Abdullah University of Science
and Technology,
Thuwal 23955-6900, Saudi Arabia
e-mails: myounis@binghamton.edu; mohammad.younis@kaust.edu.sa

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 9, 2016; final manuscript received April 13, 2017; published online June 28, 2017. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 139(5), 051008 (Jun 28, 2017) (15 pages) Paper No: VIB-16-1454; doi: 10.1115/1.4036503 History: Received September 09, 2016; Revised April 13, 2017
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Citing Articles

Vibration energy harvesting can be an effective method for scavenging wasted mechanical energy for use by wireless sensors that have limited battery life. Two major goals in designing energy harvesters are enhancing the power scavenged at low frequency and improving efficiency by increasing the frequency bandwidth. To achieve these goals, we derived a magnetoelastic beam operated at the transition between mono- and bi-stable regions. By improving the mathematical model of the interaction of magnetic force and beam dynamics, we obtained a precise prediction of natural frequencies as the distance of magnets varies. Using the shooting technique for the improved model, we present a fundamental understanding of interesting combined softening and hardening responses that happen at the transition between the two regimes. The transition regime is proposed as the optimal region for energy conversion in terms of frequency bandwidth and output voltage. Using this technique, low-frequency vibration energy harvesting at around 17 Hz was possible. The theoretical results were in good agreement with the experimental results. The target application is to power wildlife biologging devices from bird flights that have consistent high power density around 16 Hz (Shafer et al., 2015, “The Case for Energy Harvesting on Wildlife in Flight,” Smart Mater. Struct., 24(2), p. 025031).
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References

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Figures

Grahic Jump Location
Fig. 1

Schematic of the experimental setup and the stability configurations of the resonator: (a) schematic of the experimental setup and (b) monostable and bistable configurations

+Schematic of the experimental setup and the stability configurations of the resonator: (a) schematic of the experimental setup and (b) monostable and bistable configurations
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Schematic of the experimental setup and the stability configurations of the resonator: (a) schematic of the experimental setup and (b) monostable and bistable configurations
Grahic Jump Location
Fig. 2

The experimental setup of the piezoelectric energy harvesting, cantilever harvester to the right, and PUMA spectral dynamics analyzer to the left

+The experimental setup of the piezoelectric energy harvesting, cantilever harvester to the right, and PUMA spectral dynamics analyzer to the left
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The experimental setup of the piezoelectric energy harvesting, cantilever harvester to the right, and PUMA spectral dynamics analyzer to the left
Grahic Jump Location
Fig. 3

Schematic for the total magnetic force acting on the tip mass

+Schematic for the total magnetic force acting on the tip mass
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Schematic for the total magnetic force acting on the tip mass
Grahic Jump Location
Fig. 4

The tip mass static response with the separation distance, d, between the two magnets. Threshold value, dth, found to be 20 mm. Two values for monostable and bistable regions are selected for analysis.

+The tip mass static response with the separation distance, d, between the two magnets. Threshold value, dth, found to be 20 mm. Two values for monostable and bistable regions are selected for analysis.
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The tip mass static response with the separation distance, d, between the two magnets. Threshold value, dth, found to be 20 mm. Two values for monostable and bistable regions are selected for analysis.
Grahic Jump Location
Fig. 5

First normalized mode shape plotted at different distances between the two magnets, where d = 20 mm is the threshold distance

+First normalized mode shape plotted at different distances between the two magnets, where d = 20 mm is the threshold distance
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First normalized mode shape plotted at different distances between the two magnets, where d = 20 mm is the threshold distance
Grahic Jump Location
Fig. 6

Variation of the first natural frequency with the distance, d, between the two magnets. Threshold value match static profile with value of dth = 20 mm.

+Variation of the first natural frequency with the distance, d, between the two magnets. Threshold value match static profile with value of dth = 20 mm.
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Variation of the first natural frequency with the distance, d, between the two magnets. Threshold value match static profile with value of dth = 20 mm.
Grahic Jump Location
Fig. 7

Experimental and simulated forward sweep frequency and voltage responses for monostable resonator at d = 40 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

+Experimental and simulated forward sweep frequency and voltage responses for monostable resonator at d = 40 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
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Experimental and simulated forward sweep frequency and voltage responses for monostable resonator at d = 40 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 8

Experimental frequency forward swept responses for monostable resonator at d = 40 mm at different excitation levels: (a) tip mass displacement and (b) output voltage

+Experimental frequency forward swept responses for monostable resonator at d = 40 mm at different excitation levels: (a) tip mass displacement and (b) output voltage
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Experimental frequency forward swept responses for monostable resonator at d = 40 mm at different excitation levels: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 9

Experimental frequency forward swept responses for monostable resonator at d = 22 mm at different excitation levels: (a) tip mass displacement and (b) output voltage

+Experimental frequency forward swept responses for monostable resonator at d = 22 mm at different excitation levels: (a) tip mass displacement and (b) output voltage
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Experimental frequency forward swept responses for monostable resonator at d = 22 mm at different excitation levels: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 10

Experimental frequency responses for bistable resonator at d = 5 mm: (a) tip mass displacement and (b) output voltage

+Experimental frequency responses for bistable resonator at d = 5 mm: (a) tip mass displacement and (b) output voltage
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Experimental frequency responses for bistable resonator at d = 5 mm: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 11

Experimental and simulated frequency responses for bistable resonator at d = 18 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

+Experimental and simulated frequency responses for bistable resonator at d = 18 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
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Experimental and simulated frequency responses for bistable resonator at d = 18 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 12

Bistable simulated results for the nonlinear energy harvester at d = 18 mm, A = 1.0 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

+Bistable simulated results for the nonlinear energy harvester at d = 18 mm, A = 1.0 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
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Bistable simulated results for the nonlinear energy harvester at d = 18 mm, A = 1.0 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 13

The basin of attraction for the resonator for (a) d = 18 mm at 1.0 g, Ω = 18 Hz, and μ = 0.038 and (b) d = 18 mm at 1.0 g, fold frequency Ω = 16.7 Hz, and μ = 0.038. Light area is the basin of attraction for lower branch, while the dark area is the basin of attraction for the upper branch.

+The basin of attraction for the resonator for (a) d = 18 mm at 1.0 g, Ω = 18 Hz, and μ = 0.038 and (b) d = 18 mm at 1.0 g, fold frequency Ω = 16.7 Hz, and μ = 0.038. Light area is the basin of attraction for lower branch, while the dark area is the basin of attraction for the upper branch.
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The basin of attraction for the resonator for (a) d = 18 mm at 1.0 g, Ω = 18 Hz, and μ = 0.038 and (b) d = 18 mm at 1.0 g, fold frequency Ω = 16.7 Hz, and μ = 0.038. Light area is the basin of attraction for lower branch, while the dark area is the basin of attraction for the upper branch.
Grahic Jump Location
Fig. 14

Experimental frequency responses for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage

+Experimental frequency responses for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage
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Experimental frequency responses for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage
Grahic Jump Location
Fig. 15

Simulated frequency responses with shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038

+Simulated frequency responses with shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038
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Simulated frequency responses with shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038
Grahic Jump Location
Fig. 16

Simulated frequency responses with long time integration and shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038

+Simulated frequency responses with long time integration and shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038
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Simulated frequency responses with long time integration and shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038
Grahic Jump Location
Fig. 17

Maximum output voltage with increasing the resistance up to 10 MΩ for an excitation level of 0.3 g, separation distance of 18 mm, and damping of μ = 0.038

+Maximum output voltage with increasing the resistance up to 10 MΩ for an excitation level of 0.3 g, separation distance of 18 mm, and damping of μ = 0.038
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Maximum output voltage with increasing the resistance up to 10 MΩ for an excitation level of 0.3 g, separation distance of 18 mm, and damping of μ = 0.038
Grahic Jump Location
Fig. 18

The bifurcation diagram of the actuator constructed from a force (excitation level) sweep at the threshold distance (dth = 20 mm) and its natural frequency of Ω = 12.59 Hz, single-sided Poincaré sections obtained at the period of excitation

+The bifurcation diagram of the actuator constructed from a force (excitation level) sweep at the threshold distance (dth = 20 mm) and its natural frequency of Ω = 12.59 Hz, single-sided Poincaré sections obtained at the period of excitation
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The bifurcation diagram of the actuator constructed from a force (excitation level) sweep at the threshold distance (dth = 20 mm) and its natural frequency of Ω = 12.59 Hz, single-sided Poincaré sections obtained at the period of excitation
Grahic Jump Location
Fig. 19

Chaotic response for the harvester at dth = 20 mm, Ω = 12.59 Hz, and 0.2228 g excitation level: (a) phase portrait and (b) Poincaré map

+Chaotic response for the harvester at dth = 20 mm, Ω = 12.59 Hz, and 0.2228 g excitation level: (a) phase portrait and (b) Poincaré map
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Chaotic response for the harvester at dth = 20 mm, Ω = 12.59 Hz, and 0.2228 g excitation level: (a) phase portrait and (b) Poincaré map
Grahic Jump Location
Fig. 20

The bifurcation diagram sweeping the frequency of excitation at dth = 20 mm and Amp = 0.2 g, single-sided Poincaré sections obtained at the period of excitation

+The bifurcation diagram sweeping the frequency of excitation at dth = 20 mm and Amp = 0.2 g, single-sided Poincaré sections obtained at the period of excitation
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The bifurcation diagram sweeping the frequency of excitation at dth = 20 mm and Amp = 0.2 g, single-sided Poincaré sections obtained at the period of excitation
Grahic Jump Location
Fig. 21

(a) Maximum output voltage as the distance between magnets varies at the excitation level of 1.0 g and (b) dynamics behavior for energy harvester

+(a) Maximum output voltage as the distance between magnets varies at the excitation level of 1.0 g and (b) dynamics behavior for energy harvester
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(a) Maximum output voltage as the distance between magnets varies at the excitation level of 1.0 g and (b) dynamics behavior for energy harvester

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