Piezoelectric energy harvesting with a nonlinear energy sink

TLDR: In this article, a novel piezoelectric energy-harvesting device was proposed based on the principle of nonlinear energy sink and the proposed device was tested in the real world.

Abstract: This article presents a novel piezoelectric energy-harvesting device. Different from the existing designs in the literature, the proposed device is based on the principle of nonlinear energy sink i...

Figures

Figure 4.2 Time response of strongly modulated response with Ay = 0.6 m/s2, R = 1000 Ω, and Ω = 10.58 Hz: (a) amplitudes by solving Equations (4.32) to (4.35) with Matcont; (b) reconstituted responses defined by Equations (4.36) and (4.37); (c) responses by numerically integrating Equations (4.1) to (4.3).

Figure 3.26 Frequency energy plots and wavelet transform of relative displacement xa - xp from the simulation results for fp = 9 Hz: (a) low initial energy X = 0.52×10-3 (m); (b) medium initial energy X = 1.42×10-3 (m); (c) medium-high initial energy X = 2.65×10-3 (m) and (d) high initial energy X = 4.45×10-3 (m).

Figure 3.19 Experimental results with X = 4.45 mm: (a) the percentage of instantaneous energy in NES, (b) accumulated energy in NES, and (c) ratio of accumulated energy in NES to maximum of kinetic energy of NES. 3.4 Nonlinear normal mode analysis

Figure 3.9 Simulation results with X = 4.45 mm: (a) the percentage of instantaneous energy in NES, (b) accumulated energy in NES, and (c) ratio of accumulated energy in NES to maximum of kinetic energy of NES. 3.3 Experimental results

Figure 1.3 Displacement ratio of system: fn = 10.71 Hz

Figure 3.20 Frequency energy plot: backbone curves S11±

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Lakehead University
Knowledge Commons,http://knowledgecommons.lakeheadu.ca
Electronic Theses and Dissertations Electronic Theses and Dissertations from 2009
2016
Piezoelectric Energy Harvesting with a
Nonlinear Energy Sink
Zhang, Yu
http://knowledgecommons.lakeheadu.ca/handle/2453/825
Downloaded from Lakehead University, KnowledgeCommons

LAKEHEAD UNIVERSITY
Piezoelectric Energy Harvesting with a Nonlinear Energy Sink
By
Yu Zhang
A THESIS
SUBMITTED TO THE FAULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE
DEGREE OF MASTER OF SCIENCE
MECHANICAL ENGINEERING
THUNDER BAY, ONTARIO
DECEMBER, 2016
© Yu Zhang 2016

i
A
BSTRACT
Energy transfer from one system to another system, or vice versa, is happening constantly in many
processes with various forms. Vibration in machines or structures can be considered as a form of
energy transfer from a source to a receiver. In general, such vibration is unwanted. Vibration
suppression is of importance in order to protect machines or structures. To monitor vibration of a
large system such as building or bridge, a network of sensors is used. Supply of power to these
sensors is challenging due to various difficulties such as accessibility or cost. Energy harvesting
using ambient vibration is motivated to make sensors autonomous. Vibration energy can be
converted into electric energy through electromagnetic transduction or piezoelectric effect. This
research proposes a method to achieve simultaneous vibration suppression and energy harvesting
in the broadband manner.
A nonlinear energy sink (NES) is a special vibration absorber that is capable of sinking or
localizing vibration energy from a primary system. Unlike a linear or nonlinear vibration absorber,
the NES’s spring is essentially nonlinear. In this research, a variant NES is developed to achieve
vibration suppression and energy harvesting in a broad frequency band. The developed apparatus
consists of a fixed-fixed composite beam acting as the NES spring and two magnets attached at
the middle of the beam acting as the NES mass. The composite beam is formed by a thin steel
beam and two piezoelectric bimorphs attached at the ends of the steel beam. The piezoelectric
bimorphs convert the NES vibration energy into electric one. The system modeling is presented.
System identification is conducted to determine the parameter values. The transient behaviours of
the system are investigated numerically and experimentally. It has shown that the developed
apparatus demonstrates the characteristics similar to those of the NES. The harmonically forced
responses of the system are examined. The approximate analytical solutions of the steady-state
responses are derived. The Matcont is used to obtain the frequency responses plots for various
cases. An experimental study has been conducted. Both the numerical solutions and experimental
results show that the developed apparatus is capable of harvesting energy while suppressing
vibration in a wide frequency band.

ii
A
CKNOWLEDGMENTS
First, I would like to express my sincere gratitude to my supervisor Dr. Kefu Liu who saw
the potential in me and also encouraged me during the course of this research. His guidance helped
me in all aspects including thesis research and writing. I could not have imagined having a better
advisor and mentor for my master study.
I would like to also thank Kailash Batia for his assistance in the machine shop.
I would also like to thank my parents: Yurong Zhang, Heping Zhang, and Peter T. Fairchild
for supporting me in the spiritual way throughout this study and thesis writing and also my life in
general.

iii
Tab
le of Contents
ABSTRACT ......................................................................................................................... i
ACKNOWLEDGMENTS .................................................................................................. ii
Table of Contents ............................................................................................................... iii
List of Figures ......................................................................................................................v
List of Tables .......................................................................................................................x
Chapter 1
Introduction ........................................................................................................1
1.1 Overview and motivation of the research ..................................................................1
1.2 Literature review ........................................................................................................4
1.2.1 Passive vibration absorption ..............................................................................4
1.2.2 Nonlinear energy sink ........................................................................................4
1.2.3 Energy harvesting ..............................................................................................7
1.3 Objectives and contributions .....................................................................................9
1.4 Thesis outline ...........................................................................................................10
Chapter 2
Apparatus, modelling, and parameter identification ........................................11
2.1 Apparatus .................................................................................................................11
2.2 Modelling .................................................................................................................13
2.3 System parameter identification ..............................................................................13
2.3.1 Primary system parameter identification .........................................................13
2.3.2 NES system parameter identification ..............................................................15
2.4 Conclusion ...............................................................................................................19
Chapter 3
Transient responses ..........................................................................................20
3.1 Introduction ..............................................................................................................20
3.2 Simulation results ....................................................................................................20
3.3 Experimental results ................................................................................................26
3.4 Nonlinear normal mode analysis .............................................................................31
3.5 Comparison of three systems ...................................................................................38
3.6 Conclusion ...............................................................................................................48

Frequently asked questions

Q1. What have the authors contributed in "Piezoelectric energy harvesting with a nonlinear energy sink" ?

In this paper, the authors present a table of known comments and acknowledgements of the authors of this article. 

Q2. What is the way to clamp a beam?

An ideal clamping devise should allow a better beam tension control when it is loosened and achieve a secure clamped-clamped support when it is tightened. 

Q3. What is the displacement transmissibility ratio for the NES relative displacement?

Note that from hereinafter the displacement transmissibility ratio (T.R.) for the primary mass displacement is defined as Xp/Xpst while the displacement transmissibility ratio for the NES relative displacement is defined as Z/Xpst where Xpst = mpΩ2Y/kp is the static deflection of the primary spring when a force mpΩ2Y is applied. 

Q4. What is the simplest example of a nonlinear behaviour?

Figure 3.4(b) shows a clear nonlinear behaviour in which the instantaneous frequency gradually reduces and eventually becomes close to fa. 

Q5. What is the method used to analyze the harmonically forced responses of the NES systems?

Analytical solution of harmonically forced responsesCommonly the method of complexification [59] is used to analyze the harmonically forced responses of the NES systems. 

Q6. What is the effect of the NES on suppression of the peak amplitude?

It can be seen that while the NES has little effect on suppression of the peak amplitude, it does reduce the amplitude in the certain frequency region.