Piezoelectric Vibration Energy Harvesting: Modeling & Experiments

181 Pages·2018·6.153 MB·English

by  Sajid Rafique (auth.)

Sajid Rafique
Piezoelectric
Vibration Energy
Harvesting
Modeling & Experiments
Piezoelectric Vibration Energy Harvesting
fi
Sajid Ra que
Piezoelectric Vibration
Energy Harvesting
Modeling & Experiments
123
Sajid Rafique
University of Gavle
Gavle
Sweden
ISBN978-3-319-69440-5 ISBN978-3-319-69442-9 (eBook)
https://doi.org/10.1007/978-3-319-69442-9
LibraryofCongressControlNumber:2017955652
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To my beloved parents, Rafique and Salma
Preface
The recent advancements in thefieldof low powerportableelectronic devices and
microelectromechanicalsystems(MEMS)technologyhaveacceleratedresearchin
thefieldofenergyharvesting.Themainambitionistomakethemself-sufficientby
embedding an energy harvesting system within these devices, eliminating the
requirement for periodic battery replacement or recharging. The embedded energy
harvesting system can scavenge electrical energy by converting ambient energy
sourcessuchassolar,windormechanicalmotionenergy.Thisbookisfocussedon
the potential of converting mechanical motion or vibration energy into electrical
energy and also investigates the effects of energy harvesting on the overall
dynamics of the system.
Typically, there are three vibration-based energy harvesting techniques,
(1)piezoelectric,(2)electrostaticand(3)electromagnetic.Inpiezoelectricvibration
energy harvesting (PVEH), vibration energy is converted into useful electrical
energy byusing‘sensor effect’ofpiezoelectricmaterials. Theworkofthisbookis
particularly presenting close-form, more accurate, experimentally validated math-
ematical modelling techniques. Additionally, MATLAB program codes are pro-
vided to allow researchers to more easily understand and apply complex PVEH
system equations and design their own energy harvesting systems. The work pre-
sented in the book was mainly carried out during the doctorate and post-doctorate
research of the author at renowned institutes.
The overall aims of this book are manifold: (1) a thorough theoretical and
experimental analysis of a PVEH beam or assembly of beams; (2) an in-depth
analytical and experimental investigation of a dual function piezoelectric vibration
energy harvester beam/tuned vibration absorber (PVEH/TVA) or ‘electromechan-
ical TVA’; (3) example application of the dual function energy harvesting TVA to
suppress the vibration of electronic box, and (4) ready-to-run MATLAB program
codes to simulate PVEH mechanism.
vii
viii Preface
Some of the distinct features of this book can be summarised as follows:
(cid:129) An in-depth experimental validation of a PVEH beam model based on the
analytical modal analysis method (AMAM), with the investigations conducted
over a wider frequency range than previously tested.
(cid:129) The precise identification of the electrical loads that harvest maximum power
and that induce maximum electrical damping.
(cid:129) A thorough investigation of the influence of mechanical damping on PVEH
beams.
(cid:129) A procedure for the exact modelling of PVEH beams, and assemblies of such
beams, using the dynamic stiffness matrix (DSM) method.
(cid:129) A procedure to enhance the power output from a PVEH beam through the
application of a tip rotational restraint and the use of segmented electrodes.
(cid:129) The theoretical basis for the concept of a dual function PVEH beam/TVA, and
its realisation and experimental validation for a prototype device.
(cid:129) A theoretical example illustrating the application of a dual function device to
control the vibration of electronic box.
(cid:129) An improved electrical circuit configuration is presented using the real time
nonlinear electrical load.
(cid:129) Easytouseprogrammingcodestorunsimulationsandobservethebehaviourof
dual function energy harvester tuned vibration absorbers.
Gavle, Sweden Sajid Rafique
Acknowledgements
First and foremost, I would like to offer my profound gratitude to Dr. Philip
Bonello, Reader/Associate Professor, School of Mechanical, Aerospace and Civil
EngineeringatTheUniversityofManchester,forhispreciousguidanceandsupport
throughout my doctorate research work. His genuine interest in this field and his
creative ideas enhanced my vision and analytical ability.
Iwouldalsoliketoexpressmygratitudetoallthetechnicianswhohelpedmein
building the experimental set-up. I would also like to thank my friends and col-
leagues, who made this journey memorable and exciting.
Last but not the least, my parents and beloved family, I love you all and would
not have done it without your support.
ix
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background of PVEH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Aims and Objectives of the Book . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Major Contributions of the Book. . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Overall Structure of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Overview of Vibration Energy Harvesting . . . . . . . . . . . . . . . . . . . . 9
2.1 Background of Energy Harvesting. . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Energy Harvesting from Vibrations . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Piezoelectric Vibration Energy Harvesting (PVEH). . . . . . . . . . . . 12
2.3.1 Improvements in Modelling Techniques . . . . . . . . . . . . . . 13
2.3.2 Progress in Geometric Configuration of Piezoelectric
Harvester. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 Application of PVEH in Vibration Control . . . . . . . . . . . . 21
2.3.4 Application of PVEH in Nanogenerators. . . . . . . . . . . . . . 26
2.4 Chapter Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Distributed Parameter Modelling and Experimental Validation . . . . 31
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Modelling of a Bimorph Using Distributed Parameters . . . . . . . . . 32
3.2.1 Mechanical Model with Electrical Coupling Effects. . . . . . 33
3.2.2 Electrical Circuitry Equation with Backward
Mechanical Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Derivation of FRFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.4 Reduced Expressions of FRFs for a Single Mode . . . . . . . 39
3.2.5 Application to Non-Harmonic Base Excitation. . . . . . . . . . 40
3.3 Experimental Validation of the Model . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Mechanical Damping Estimation . . . . . . . . . . . . . . . . . . . 42
xi
xii Contents
3.3.2 Comparison of Experimental and Theoretical FRFs . . . . . . 46
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Modelling of Energy Harvesting Beams Using Dynamic Stiffness
Method (DSM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1 General Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.2 Dynamic Stiffness Method (DSM) . . . . . . . . . . . . . . . . . . 63
4.2.3 Analytical Modal Analysis Method (AMAM) . . . . . . . . . . 66
4.3 Theoretical Analysis of Cantilevered Bimorph . . . . . . . . . . . . . . . 69
4.3.1 Verification: DSM Vs AMAM . . . . . . . . . . . . . . . . . . . . . 70
4.3.2 Effect of Electrical Impedance . . . . . . . . . . . . . . . . . . . . . 71
4.3.3 Effect of Mechanical Damping . . . . . . . . . . . . . . . . . . . . . 75
4.3.4 Duality of Energy Harvesting Beam and Vibration
Neutraliser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.5 Effect of Damping-Related Assumptions. . . . . . . . . . . . . . 79
4.4 Extension of DSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.1 One-Dimensional Assembly of Beam Segments. . . . . . . . . 80
4.4.2 Other Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 A Theoretical Analysis of an ‘Electromechanical’ Beam Tuned
Mass Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1.1 Distinct Aspects of This Chapter’s Work . . . . . . . . . . . . . 90
5.2 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.1 Benchmark Model and Its Validation . . . . . . . . . . . . . . . . 92
5.2.2 Derivation of Coupled Electromechanical Receptance
of TMD by AMAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2.3 Derivation of Electromechanical TMD Receptance
Using DSM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3 Simulations: FRFs of Host with Energy Harvesting TVA . . . . . . . 108
5.3.1 Double Circuit: Coupled FRFs for Parallel R-L-C
Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3.2 Double Circuit: Coupled FRFs for Parallel C and
Series R-L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.3.3 Single Circuit: Coupled FRFs. . . . . . . . . . . . . . . . . . . . . . 118
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121