Design And Characterization On Piezoelectric Cantilever As A Self-Powered Accelerometer.
DESIGN AND CHARACTERIZATION ON
PIEZOELECTRIC CANTILEVER
AS A SELF-POWERED ACCELEROMETER
BONG YU JING
MASTER OF SCIENCE IN
ELECTRONIC ENGINEERING
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Faculty
of
Electronics
and Computer Engineering
DESIGN AND CHARACTERIZATION ON
PIEZOELECTRIC CANTILEVER
AS A SELF-POWERED ACCELEROMETER
Bong Yu Jing
Master of Science in Electronic Engineering
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DESIGN AND CHARACTERIZATION ON PIEZOELECTRIC CANTILEVER AS A SELF-POWERED ACCELEROMETER
BONG YU JING
A thesis submitted
in fulfilment of the requirements for the degree of Master of Science in Electronic Engineering
Faculty of Electronic and Computer Engineering
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
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DECLARATION
I declare that this thesis entitled “Design and Characterization on Piezoelectric Cantilever
as a Self-Powered Accelerometer” is the result of my own research except as cited in the
references. The thesis has not been accepted for any degree and is not concurrently
submitted in candidature of any other degree.
Signature : ...
Name : ...
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APPROVAL
I hereby declare that I have read this thesis and in my opinion this thesis is sufficient in
terms of scope and quality for the award of Master of Science in Electronic Engineering.
Signature : ...
Supervisor Name : ...
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ABSTRACT
Piezoelectric cantilever working on direct piezoelectric effect has shown promising applications as a sensor as well as a micro-power generator depending on the amount of stress that is applied on the piezoelectric material at different range of frequencies. In this research, a self-powered accelerometer that consists of a wide-band energy harvesting power generator, a low operating frequency device acceleration sensor, and a signal conditioning circuit is designed. Piezoelectric cantilevers are being used in this research as a sensor to measure the vibration acceleration level and at the same time as a generator to power up the amplifier circuit. This research includes characterize the frequency response of the piezoelectric cantilever by altering its effective mass and length, design the self-powered accelerometer system, and lastly verify the output of the self-self-powered system with battery powered system. The result shows that increasing the effective mass of the cantilever can reduce the resonant frequency of the cantilever, while reducing the effective length of the cantilever would increase the resonant frequency. The designed self-powered accelerometer is able to operate at broadened operating frequency range of 180-310 Hz with acceleration level of not lower than 0.8-g and is able to produce linear output with a sensitivity of 231.28mV/g-level. The piezoelectric generator is able to produced constant voltage output of 1.8V and power output not less than 80µW at operating condition. While for the sensor, signal is successfully amplified at a factor of 3.2 with error deviation less than 15%. The overall result is verified and shows good agreement of 5% error with conventional battery powered accelerometer system and compatible with standard vibration source.
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ABSTRAK
Piezoelektrik julur telah menunjukkan potensi yang memberangsangkan dalam aplikasi sebagai penderia dan penjana kuasa-mikro bergantung kepada jumlah tegangan yang dikenakan ke atasnya. Kajian ini melibatkan reka bentuk satu sistem terbekal diri yang terdiri daripada penjana kuasa berjalur lebar, penderia untuk mengukur magnitude getaran yang berfungsi pada frequensi rendah, dan penguat yang menguatkan isyarat penderia. kekerapan operasi yang rendah sensor pecutan peranti dan litar penyesuaian isyarat direka. Piezoelektrik julur digunakan sebagai penderia untuk mengukur magnitude getaran dan pada masa yang sama sebagai penjana kuasa dengan menggunakan sumber getaran yang sama. Kajian ini termasuk pencirian tindak balas piezoelektrik julur dengan mengubah jisim pemberat and panjang julur, mereka bentuk sistem terbekal diri yang mengukur magnitude getaran, dan akhir sekali mengesahkan output sistem terbekal diri tersebut dengan sistem bateri.. Hasil kajian menunjukkan peningkatan jisim julur boleh mengurangkan frekuensi salunannya, manakala mengurangkan panjang julur akan meningkatkan frekuensi salunannya. Sistem yang direka berupaya untuk beroperasi pada frekuensi 180-310 Hz dengan magnitude getaran tidak kurang daripada 0.8-g dan mampu menghasilkan output linear dengan kepekaan 231.28mV/g. Penjana kuasanya mampu menghasilkan voltan 1.8V dan kuasa tidak kurang daripada 80μW. Manakala, isyarat yang dihasilkan oleh penderia berjaya dikuatkan pada faktor 3.2 dengan ralat tidak melebihi 15%. Keputusan keseluruhan telah disahkan dan menunjukkan hasil yang baik iaitu degan ralat tidak melebihi 5% apabila dibandingkan dengan sistem sedia ada yang beroperasi menggunakan bateri.
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ACKNOWLEDGEMENT
I would like to express my utmost gratitude and appreciation to my supervisor, Dr
Kok Swee Leong for his guidance throughout my graduate career. I truly appreciate his
passion, patience and kindness that have made completing this dissertation a pleasure.
Thanks also go to my co-supervisor, Dr. Mohd Shakir bin Md Saat for his helpful
feedbacks and recommendations in this research.
Thanks are accorded to the financial support from Universiti Teknikal Malaysia
Melaka (UTeM) for the scholarship award. Besides that, thanks for providing a great
research environment and facilities for me to complete this research. I also like to
acknowledge Mdm. Hafizah bte Adnan, Assistance Engineer for Electronics Industry
Laboratory for her great cooperation and commitment in the laboratory session for this
research. Also thanks to my fellow friends for their help and support.
Finally, my exceptional and grateful thanks also accorded to my beloved, parents
and family members for giving me their endless support and motivation during my times of
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TABLE OF CONTENTS PAGE DECLARATION APPROVAL ABSTRACT i ABSTRAK ii ACKNOWLEDGEMENT iii
TABLE OF CONTENTS iv
LIST OF TABLES vii
LIST OF FIGURES viii
LIST OF APPENDICES xiv
LIST OF ABBREVIATIONS xv
LIST OF SYMBOLS xvii
LIST OF PUBLICATIONS xix
CHAPTER
1. INTRODUCTION 1
1.0Overview 1
1.1Problem Statement 4
1.2Objectives 6
1.3Scope of Work 7
1.4Contributions 8
1.5Thesis Outlines 9
2. LITERATURE REVIEW 11
2.0Introduction 11
2.1Piezoelectricity 12
2.1.1 Discovery of Piezoelectricity 12 2.1.2 Development of Piezoelectricity 13 2.1.3 Basic Operations of Piezoelectricity 16 2.1.4 Types of Piezoelectric Materials and Structures 18 2.1.5 Direct and Converse Piezoelectric Effects 20 2.1.6 Piezoelectric Integrated Cantilever Structure 22 2.1.7 Resonant Frequency Tuning 24
2.2Applications of Piezoelectricity 28 2.2.1 Generator - Energy Harvester 29
2.2.2 Sensor - Accelerometer 30 2.2.2.1 Principle of Piezoelectric Accelerometer 31 2.2.2.2 Frequency Range of Piezoelectric Accelerometer 32 2.2.2.3 Structural Design of Piezoelectric Accelerometer 33 2.2.2.4 Advantages of Piezoelectric Accelerometer 36
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2.3Signal Conditioning Circuit – Op-amp 37 2.4Chapter Summary 39
3. METHODOLOGY 41
3.0 Introduction 41
3.1 Preliminary Experiment 44 3.1.1 Clamping Method Identification for Error Minimization 46 3.1.2 Frequency Response Identification of Piezoelectric Cantilevers 47
(Open Circuit Voltage)
3.1.3 Impedance Matching Method 49 3.1.4 Frequency Response Identification of Piezoelectric Cantilevers 49 (Power)
3.2 Piezoelectric Cantilevers as Micro-power Generator 50 3.2.1 Proof Masses Verification 51 3.2.2 Frequency Response Measurement for Multiple Cantilevers 52 3.2.3 Impedance Matching for Multiple Cantilevers 53 3.2.4 Performance Determination of Connected Multiple Cantilevers 56 3.2.5 Phase Shift Measurement Method 57 3.2.6 Performance Measurement of the Generator after Rectification 58 3.3 Piezoelectric Cantilevers as Sensor 59 3.3.1 Output Response Identification of Piezoelectric Cantilevers 59 (Acceleration Level)
3.3.2 Frequency Response Identification of Piezoelectric Cantilever 60 With Length Variation
3.3.3 Output Response Identification of Altered Piezoelectric Cantilevers 61 (Acceleration Level)
3.4 Self-powered System Integration 62 3.4.1 Final Result Compilation of the Overall System 63 3.4.2 Result Verification Method 64 3.5 Chapter Summary 64
4. RESULT AND DISCUSSION 66
4.0 Introduction 66
4.1 Preliminary Experiment Results (Preparation) 66 4.1.1 Clamping Error Identification and Minimization 66 4.1.2 Frequency Response of Piezoelectric Cantilevers 72
(Open Circuit Voltage)
4.1.3 Impedance Matching Result 73 4.1.4 Frequency Response of Piezoelectric Cantilevers (Power Output) 76 4.2 Piezoelectric Cantilevers as Micro-power Generator 78 4.2.1 Proof Masses Variation Responses 78 4.2.2 Frequency Response for Multiple Cantilevers 80 4.2.3 Impedance Matching for Multiple Cantilevers 84
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4.2.3.1 Series Connection with Same Polarity 84 4.2.3.2 Series Connection with Alternating Polarities 87 4.2.3.3 Parallel Connection with Same Polarity 89 4.2.3.4 Parallel Connection with Alternating Polarities 91 4.2.4 Performance Measurement of Connected Multiple Cantilevers 93 4.2.4.1 Series Connection with Same Polarity 94 4.2.4.2 Series Connection with Alternating Polarities 96 4.2.4.3 Parallel Connection with Same Polarity 98 4.2.4.4 Parallel Connection with Alternating Polarities 101 4.2.5 Phase Shifting of Cantilever with Proof Mass 103 4.2.6 Performance of the Generator after Rectification 105 4.3 Piezoelectric Cantilevers as Sensor 108 4.3.1 Output Response of Piezoelectric Cantilevers (Acceleration Level) 108 4.3.2 Frequency Response Piezoelectric Cantilever with Length Variation 109 4.3.3 Output Response of Altered Piezoelectric Cantilever 112 (Acceleration Level)
4.4 System Integration Performance Result 114 4.5 Chapter Summary 119
5. CONCLUSION 121
5.0 Introduction 121
5.1 Summary of Work 121 5.1.1 Preliminary Experiment 121 5.1.2 Piezoelectric Cantilevers as Micro-power Generator 122 5.1.3 Piezoelectric Cantilevers as Acceleration Sensor 123 5.1.4 Overall Integrated System 124
5.2 Future Work 124
5.2.1 Widen the Operating Frequency of the Generator 124 5.2.2 Wireless Application of Overall System 125
REFERENCES 126 APPENDICES 133
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LIST OF TABLES
TABLE TITLE PAGE
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LIST OF FIGURES
FIGURE TITLE PAGE
2.1 Piezoelectric Direct Effect in an Open Circuit Configuration 17
2.2 Piezoelectric Direct Effect in Short Circuit Configuration 17
2.3 Schematic Diagram of the Electrical Domain (a) Before Polarization, (b) During Polarization and (c) After Polarization
18
2.4 Electromechanical Conversion through Piezoelectricity Phenomenon (Minazara et al, 2008)
20
2.5 Notation of Piezoelectric Axes 21
2.6 Cross-sectional View of Piezoelectric Configuration Mode, (a) ݀ଷଵMode and (b) ݀ଷଷMode
22
2.7 Types of Piezoelectric Cantilever 23
2.8 Piezoelectric based Cantilever with ݀ଷଵConfiguration 23 2.9 Piezoelectric based Cantilever with ݀ଷଷConfiguration 24 2.10 Illustration of Measurement Variables of Piezoelectric Cantilever 25
2.11 Hierarchy of Main Energy Harvesting Technologies 29
2.12 Illustration of Piezoelectric Active Element 31
2.13 Illustration for Principle of Piezoelectric Accelerometer 32
2.14 Frequency Response Curve 33
2.15 Basic Structural Design of Piezoelectric Accelerometer 34
2.16 Standard Symbol of Operational Amplifier 37
2.17 Inverting Configuration for Op-amp 38
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3.1 Flowchart for Research Methodology 42
3.2 Overall Experiment Set-up 43
3.3 Electrical to Mechanical to Electrical Conversion Mechanism 44
3.4 Piezoelectric Cantilevers with Similar Length but Different Width (Piezo System Inc, 2011)
45
3.5 Illustrations for the Different Clamping Methods (a) Using Screw (b) Using 1mm thickness Plasticine (c) Using 2mm thickness Plasticine
46
3.6 Illustration and Actual Photo indicating the Clamping Locations 47
3.7 Illustration and Actual Photo indicating the Clamping Location of Cantilever CS, CM, and CL
48
3.8 Illustration of the Experiment Set-up for Frequency Response of Piezoelectric Cantilevers (Voltage)
48
3.9 Illustration of the Experiment Set-up for Impedance Matching 49
3.10 Illustration of the Experiment Set-up for Frequency Response of Piezoelectric Cantilevers (Power)
50
3.11 Illustration of the Experiment Set-up for Proof Mass Verification 51
3.12 Photo of Cantilever CS, CM and CL before and after Proof Masses are added
53
3.13 Illustrations for the type of Connections 55
3.14 Illustration of phase shift measurement by using (a) Time Different Method and (b) Lissajous Pattern Method
57
3.15 Illustration of Experimental Set-up for Linearity Test 60
3.16 Illustration for Reducing Cantilever Length by Clamping Over 61
3.17 Illustration of Experimental Set-up for Linearity Test after Length Reduction
62
3.18 Block Diagram of the Overall System 63
3.19 Circuit Diagram of the Overall System 63
4.1 Box Plot for Frequency Responses of Cantilever CS Clamped at Location A Using Screw, Plasticine with 1mm Thickness, or Plasticine with 2mm Thickness Respectively
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4.2 Box Plot for Frequency Responses of Cantilever CM Clamped at Location A Using Screw, Plasticine with 1mm Thickness, or Plasticine with 2mm Thickness Respectively
67
4.3 Box Plot for Frequency Responses of Cantilever CL Clamped at Location A using Screw, Plasticine with 1mm Thickness, or Plasticine with 2mm Thickness Respectively
68
4.4 Box Plot for Frequency Responses of Cantilever CS Clamped at Location A, B and C using Plasticine (1mm Thickness)
70
4.5 Box Plot for Frequency Responses of Cantilever CM Clamped at Location A, B and C using Plasticine (1mm Thickness).
70
4.6 Box Plot for Frequency Responses of Cantilever CL Clamped at Location A, B and C using Plasticine (1mm Thickness)
71
4.7 Frequency Responses for Cantilever CS, CM, and CL Respectively when Clamped at Location A, B and C using 1mm Plasticine
72
4.8 Output Responses (Voltage) for Cantilever CS, CM, and CL Respectively with Varies Load Resistance
74
4.9 Output Responses (Power) for Cantilever CS, CM, and CL Respectively with Varies Load Resistance
75
4.10 Output Response (Power) for Cantilever CS with Varies Load Resistance
75
4.11 Frequency Responses (Voltage) for Cantilever CS, CM, and CL respectively when connected to matching Load Resistance
76
4.12 Frequency Responses (Power) for Cantilever CS, CM, and CL respectively when connected to matching Load Resistance
77
4.13 Frequency Responses(Voltage) for Cantilever CL when Different Proof Mass is Added
78
4.14 Comparison of Experimental and Theoretical Resonance Frequency Shift based on Proof Mass Weight
79
4.15 Frequency Response in term of Output Voltage for Same Size Multiple Cantilevers
81
4.16 Frequency Response in term of Output Power for Same Size Multiple Cantilevers
81
4.17 Frequency Response in term of Output Voltage for Multiple Cantilevers with Proof Mass
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4.18 Frequency Response in term of Output Power for Multiple Cantilevers with Proof Mass
83
4.19 Output Responses (Voltage) toward Varies of Load Resistance for Cantilevers Connected in Series with Same Polarity Connection
85
4.20 Output Responses (Power) toward Varies of Load Resistance for Cantilevers Connected in Series with Same Polarity Connection
86
4.21 Output Responses (Voltage) toward Varies of Load Resistance for Cantilevers Connected in Series with Alternating Polarities Connection
87
4.22 Output Responses (Power) toward Varies of Load Resistance for Cantilevers Connected in Series with Alternating Polarities Connection
88
4.23 Output Responses (Voltage) toward Varies of Load Resistance for Cantilevers Connected in Parallel with Same Polarity Connection
89
4.24 Output Responses (Power) toward Varies of Load Resistance for Cantilevers Connected in Parallel with Same Polarity Connection
90
4.25 Output Responses (Voltage) toward Varies of Load Resistance for Cantilevers Connected in Parallel with Alternating Polarities Connection
91
4.26 Output Responses (Power) toward Varies of Load Resistance for Cantilevers Connected in Parallel with Alternating Polarities Connection
92
4.27 Frequency Responses (Voltage) for Cantilevers Connected in Series with Same Polarity Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
94
4.28 Frequency Responses (Power) for Cantilevers Connected in Series with Same Polarity Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
95
4.29 Frequency Responses (Voltage) for Cantilevers Connected in Series with Alternating Polarities Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
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4.30 Frequency Responses (Power) for Cantilevers Connected in Series with Alternating Polarities Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
98
4.31 Frequency Responses (Voltage) for Cantilevers Connected in Parallel with Same Polarity Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
99
4.32 Frequency Responses (Power) for Cantilevers Connected in Parallel with Same Polarity Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
100
4.33 Frequency Responses (Voltage) for Cantilevers Connected in Parallel with Alternating Polarities Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
101
4.34 Frequency Responses (Power) for Cantilevers Connected in Parallel with Alternating Polarities Connection. (a) Two cantilevers are connected. (b) Three cantilevers are connected. (c) Four cantilevers are connected
102
4.35 Phase shift of Cantilevers with Proof Mass Attached obtained using Time Different Method
104
4.36 Phase shift of Cantilevers with Proof Mass Attached obtained using Lissajous Pattern Method
104
4.37 Frequency Response in term of Output Voltage Obtained Before and After Rectified Using LTC3588-1
106
4.38 Frequency Response in term of Output Power Obtained Before and After Rectified Using LTC3588-1
106
4.39 Output Voltage obtained after rectified with LTC3588-1 under Variation of Acceleration Level
107
4.40 Output Voltage obtained under Variation of Acceleration Level 109
4.41 Output Voltage obtained under Variation of Acceleration Level with Trendline and Error Bar
109
4.42 Frequency Response of the Cantilever after Length Reduction 110
4.43 Theoretical and Experimental Results for Effect of Length Reduction of Cantilevers toward its Resonance Frequency
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4.44 Output Voltage obtained under Variation of Acceleration Level after Resonance Frequency Alteration
113
4.45 Actual Photo of the Complete System 114
4.46 Frequency Response Curve for Designed Generator and Sensor 115
4.47 Enlarged Frequency Response Curve for Designed Generator and Sensor
116
4.48 Output Signal Voltage in Response of Different Acceleration Level 117
4.49 Output Signal Voltage Before and After Amplification in Response of Different Acceleration Level
118
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LIST OF APPENDICES
APPENDIX TITLE
A1 Datasheet of Piezoelectric Cantilevers
A2 Datasheet of LTC3588-1
A3 Datasheet of TS1001
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LIST OF ABBREVIATIONS
ABBREVIATION DESCRIPTION
MEMS Micro-Electro-Mechanical-System
AC Alternating Current
CS Small Sized Cantilever (Q220-A4-103YB)
CM Medium Sized Cantilever (Q220-A4-203YB)
CL Large Sized Cantilever (Q220-A4-303YB)
CL1 Additional Large Sized Cantilever 1
CL2 Additional Large Sized Cantilever 2
CL3 Additional Large Sized Cantilever 3
CL1p CL1 with Proof Mass Attached (0.15g)
CL2p CL2 with Proof Mass Attached (0.50g)
CL3p CL3 with Proof Mass Attached (1.00 g)
CC Large Sized Cantilever that Act as Constant Cantilever
CLa Large Sized Cantilever that Act as Accelerometer
DC Direct Current
LTC3588-1 Nanopower Energy Harvesting Power Supply
PVDF Polyvinylidenedifluoride
PZT Lead Zirconium Titanite
RF Radio Frequency
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SiO2 Silicon Dioxide
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LIST OF SYMBOLS
SYMBOL UNIT DESCRIPTION
δ m Distance from Neutral Axis to the Centroid of Piezoelectric Layer
d dimensionless Piezoelectric Constant Matrix
D C/m2 Electric Displacement
ߝ் F/m Permittivity Matrix at Constant Stress
ܧ N/m Elastic Modulus for Electrode Layer
ܧ N/C Electric Field
݂ Hz Natural Frequency
݂௪ Hz New Resonant Frequency
݄ m Total Thickness of the Beam
ܫ m4 Area moment of Inertia
݇ N/m Equivalent Stiffness
݇௪ N/m New Stiffness of the Beam
݈ m Length of the Beam
݈௪ m New Effective Length of the Beam
݉ Kg Total Beam Mass
݉ Kg Effective Mass
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Included
ߩ Kg/m3 Density of the Beam
ܲ N Force at that Particular Point
ݏா m2/N Matrix of Compliance Coefficients at
Constant Electric Field Strength
S dimensionless Strain
t dimensionless Transposition of a Matrix
T N/m2 Stress
ݓ m Width of the Beam
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LIST OF PUBLICATIONS
JOURNAL
[1] Bong, Y.J. and Kok, S.L., 2015.Characterization on Piezoelectric Cantilever for Its
Linear Response at Low Frequency for Measuring Acceleration Level of Vibration.
Applied Mechanics and Materials, 761, pp.579-583.
CONFERENCE PROCEEDINGS
[1] Bong, Y.J. and Kok, S.L., 2013.Demonstration of Self-Powered Accelerometer Using
Piezoelectric Micro-Power Generator. In: IEEE Student Conference on Research and
Development (SCOReD) 2013, Putrajaya, Malaysia, 16-17December 2013. IEEE
Publisher.
[2] Bong, Y.J. and Kok, S.L., 2014.Characterization on Piezoelectric Cantilever for Its
Linear Response at Low Frequency for Measuring Acceleration Level of Vibration. In:
International Conference on Design and Concurrent Engineering (iDECON) 2014,
Melaka, Malaysia, 22-23September 2014.
[3] Bong, Y.J., Kok, S.L. and Thong, L.W., 2014.Experimental Verification of Wide-Band
Energy Harvesting using Piezoelectric Multi-cantilever with Resonant Frequency
Variation. In: Malaysian Technical Universities Conference on Engineering and
(1)
LIST OF APPENDICES
APPENDIX TITLE
A1 Datasheet of Piezoelectric Cantilevers
A2 Datasheet of LTC3588-1
A3 Datasheet of TS1001
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xv
LIST OF ABBREVIATIONS
ABBREVIATION DESCRIPTION
MEMS Micro-Electro-Mechanical-System
AC Alternating Current
CS Small Sized Cantilever (Q220-A4-103YB) CM Medium Sized Cantilever (Q220-A4-203YB) CL Large Sized Cantilever (Q220-A4-303YB) CL1 Additional Large Sized Cantilever 1 CL2 Additional Large Sized Cantilever 2 CL3 Additional Large Sized Cantilever 3 CL1p CL1 with Proof Mass Attached (0.15g) CL2p CL2 with Proof Mass Attached (0.50g) CL3p CL3 with Proof Mass Attached (1.00 g)
CC Large Sized Cantilever that Act as Constant Cantilever CLa Large Sized Cantilever that Act as Accelerometer
DC Direct Current
LTC3588-1 Nanopower Energy Harvesting Power Supply
PVDF Polyvinylidenedifluoride
PZT Lead Zirconium Titanite
RF Radio Frequency
(3)
SiO2 Silicon Dioxide
(4)
xvii
LIST OF SYMBOLS
SYMBOL UNIT DESCRIPTION
δ m Distance from Neutral Axis to the Centroid
of Piezoelectric Layer
d dimensionless Piezoelectric Constant Matrix
D C/m2 Electric Displacement
ߝ் F/m Permittivity Matrix at Constant Stress
ܧ N/m Elastic Modulus for Electrode Layer
ܧ N/C Electric Field
݂ Hz Natural Frequency
݂௪ Hz New Resonant Frequency
݄ m Total Thickness of the Beam
ܫ m4 Area moment of Inertia
݇ N/m Equivalent Stiffness
݇௪ N/m New Stiffness of the Beam
݈ m Length of the Beam
݈௪ m New Effective Length of the Beam
݉ Kg Total Beam Mass
݉ Kg Effective Mass
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Included
ߩ Kg/m3 Density of the Beam
ܲ N Force at that Particular Point
ݏா m2/N Matrix of Compliance Coefficients at
Constant Electric Field Strength
S dimensionless Strain
t dimensionless Transposition of a Matrix
T N/m2 Stress
ݓ m Width of the Beam
(6)
xix
LIST OF PUBLICATIONS
JOURNAL
[1] Bong, Y.J. and Kok, S.L., 2015.Characterization on Piezoelectric Cantilever for Its Linear Response at Low Frequency for Measuring Acceleration Level of Vibration.
Applied Mechanics and Materials, 761, pp.579-583.
CONFERENCE PROCEEDINGS
[1] Bong, Y.J. and Kok, S.L., 2013.Demonstration of Self-Powered Accelerometer Using Piezoelectric Micro-Power Generator. In: IEEE Student Conference on Research and
Development (SCOReD) 2013, Putrajaya, Malaysia, 16-17December 2013. IEEE
Publisher.
[2] Bong, Y.J. and Kok, S.L., 2014.Characterization on Piezoelectric Cantilever for Its Linear Response at Low Frequency for Measuring Acceleration Level of Vibration. In:
International Conference on Design and Concurrent Engineering (iDECON) 2014,
Melaka, Malaysia, 22-23September 2014.
[3] Bong, Y.J., Kok, S.L. and Thong, L.W., 2014.Experimental Verification of Wide-Band Energy Harvesting using Piezoelectric Multi-cantilever with Resonant Frequency Variation. In: Malaysian Technical Universities Conference on Engineering and