Piezoelectric Ceramic Resonators (eBook)

Jiří Erhart, Petr Půlpán, Martin Pustka (Autoren)

eBook Download: PDF

2016 | 1st ed. 2017
XVII, 251 Seiten
Springer International Publishing (Verlag)
978-3-319-42481-1 (ISBN)

Infos

This book helps the reader to understand the specific properties of piezoelectric ceramic resonators. It provides their theoretical description by immitance and equivalent circuit method. The nummerical modelling described is accompanied by examples of properties measured experimentally. Piezoelectric ceramic transformers are also covered, followed by a series of solved and unsolved problems prepared specially for students. 

Prof. Jiří Erhart works at the Technical University of Liberec and at the research institute VÚTS, a.s. in Liberec, Czech Republic. He is the Head of the Piezoelectricity Research Laboratory at the Department of Physics and his reasearch interests are on piezoelectricity and piezoelectric materials, ferroelectric domains and domain engineering, piezoelectric ceramics transformers, resonators, and actuators.

Petr Půlpán, Ph.D, work at the R&D Measurements department, VÚTS a.s., Liberec, Czech Republic. His main research interests are in electromechanical properties of ceramics, design of piezoelectric transducers and actuators, and general acoustics and vibrations.

Martin Pustka, works at VÚTS, a.s. Liberec, R&D Department Measurements, and is the Head of the NVH group. His primary research interests are noise and vibration measurement and analysis, structural dynamics, piezoelectric resonators and application of piezoelectric resonant structures.

Inhalt

Preface 6
Contents 11
List of symbols 15
1 Piezoelectricity and Piezoelectric Properties 18
1.1 Pyroelectricity 18
1.2 Piezoelectricity Discovery 19
1.3 Ferroelectricity Discovery 20
1.4 Piezoelectric Properties 21
References 26
2 Piezoelectric Ceramic Materials 27
2.1 PZT Ceramics 29
2.2 Other Ceramic Compositions 34
2.3 Example of Crystallographic Symmetry for Mechanically Textured Ceramics 36
References 42
3 Piezoelectric Ceramic Resonators (Resonance Frequency and Equivalent Electrical Circuit) 44
3.1 Introduction 44
3.1.1 Basic Assumptions and Approximations 44
3.1.2 Solution of Free Vibrations 45
3.1.3 Electromechanical Coupling Factor 47
3.1.4 Electrical Equivalent Circuit 50
3.2 Length Extensional Mode (Side Electrodes) 54
3.2.1 Solution of Free Vibrations 54
3.2.2 Parameters of Electrical Equivalent Circuit 56
3.3 Length Extensional Mode (End Electrodes) 62
3.3.1 Solution of Free Vibrations 62
3.3.2 Parameters of Electrical Equivalent Circuit 65
3.4 Thickness Shear Mode (Side Electrodes) 68
3.4.1 Solution of Free Vibrations 68
3.4.2 Parameters of Electrical Equivalent Circuit 70
3.5 Thickness Shear Mode (End Electrodes) 73
3.5.1 Solution of Free Vibrations 73
3.5.2 Parameters of Electrical Equivalent Circuit 74
3.6 Thickness Extensional Mode 76
3.6.1 Solution of Free Vibrations 76
3.6.2 Parameters of Electrical Equivalent Circuit 78
3.7 Radial Mode of Circular Plate 81
3.7.1 Solution of Free Vibrations 81
3.7.2 Parameters of Electrical Equivalent Circuit 83
3.7.3 Solution Using Planar Material Constants 85
3.8 Radial Mode of Circular Rod 88
3.8.1 Solution of Free Vibrations 88
3.8.2 Parameters of Electrical Equivalent Circuit 90
3.9 Contour Extensional Mode of Square Plate 95
3.9.1 Solution of Free Vibrations 95
3.9.2 Parameters of Electrical Equivalent Circuit 96
3.10 Width Extensional Mode 99
3.10.1 Solution of Free Vibrations 99
3.10.2 Parameters of Electrical Equivalent Circuit 101
3.11 Width Extensional Mode (Side Electrodes) 103
3.11.1 Solution of Free Vibrations 103
3.11.2 Parameters of Electrical Equivalent Circuit 104
3.12 Thickness Extensional Mode (Side Electrodes) 107
3.12.1 Solution of Free Vibrations 107
3.12.2 Parameters of Electrical Equivalent Circuit 108
3.13 Width Extensional Mode (End Electrodes) 111
3.13.1 Solution of Free Vibrations 111
3.13.2 Parameters of Electrical Equivalent Circuit 113
3.14 Radial Axisymmetric Vibrations of Rings and Tubes 115
3.14.1 Radial Mode of Thin Rings 116
3.14.2 Radial Mode of Axially Polarized Ring 120
3.14.3 Radial Mode of Radially Polarized Ring 125
3.15 Miscellaneous Vibration Modes 128
3.16 Approximative Theories for the Solution of Piezoelectric Resonator Vibrations 129
References 132
4 Applications of Piezoelectric Resonators 134
4.1 Introduction 134
4.2 Impedance Spectrum Characteristics 135
4.3 Electromechanical Coupling Factor 139
4.4 Material Property Measurement for Piezoelectric Ceramics 143
4.4.1 Thickness Poled Bar with Electrodes on Major Faces (/varvec {k}_{31}-mode) 143
4.4.2 Longitudinally Poled Bar with Electrodes at the Ends ({/varvec k}_{/bf 33}-mode) 147
4.4.3 Longitudinally Poled Bar or Plate with Electrodes on Major Faces ({/varvec k}_{/bf 15}-mode) 148
4.4.4 Thickness Poled Disc — Thickness Extensional Mode ({/varvec k}_{{/varvec t}}-mode) 149
4.4.5 Thickness Poled Disc — Radial Mode ({/varvec k}_{/varvec p}-mode) 150
4.4.6 Combination of Coefficients Measured at Different Vibration Modes 152
4.4.7 Poisson’s Ratio Measurement 153
4.5 Measurement Accuracy of the Electromechanical Tensors for Piezoelectric Ceramics 158
4.5.1 Bar, {/varvec k}_{{{{/bf 31}}}}-mode 158
4.5.2 Bar, {/varvec k}_{/bf 33}-mode 159
4.5.3 Disc, {/varvec k}_{/varvec p}-mode 160
4.5.4 Disc, {/varvec k}_{{/varvec t}}-mode 161
4.5.5 Plate or Bar, {/varvec k}_{/bf 15}-mode 162
4.6 Temperature Stability of Resonance Frequency for Ceramic Resonators 163
References 166
5 Piezoelectric Transformers 169
5.1 Piezoelectric Transformer Design 170
5.2 Piezoelectric Transformer Modeling 178
5.2.1 Bar Rosen type Transformer ( {/bi k}_{/bf 31} - /bi k_{/bf 33}} Mode) 181
5.2.2 Bar 2-Segment or 3-Segment Electrode Transformer ( /bi k_{/bf 31} -/bi k_{/bf 31} Mode) 186
5.2.3 Bar 2-Segment Electrode Transformer with Longitudinal Poling ({/bi k}_{/bf 33} /bf - {/bi k}_{/bf 33} Mode) 192
5.2.4 Disc Ring-Dot Transformer (/bi {k_{p} - k_{p}} Mode) 197
5.2.5 Disc Ring-Dot Transformer Made from Two Different Materials (/bi {k_{p} - k_{p}} Mode) 201
5.2.6 Disc Rosen type Transformer ({/bi k_{p}} - /bi k_{/bf 33} Mode) 205
5.2.7 Ring Rosen type Transformer (/bi k_{p} - k_{/bf 33} Mode) 209
5.2.8 Double Ring Electrode Ring Transformer (/bi k_{p} - k_{p} Mode) 214
References 217
Appendix A — Material Tensors 221
Appendix B — Solution in Cartesian Coordinates 245
B.1 General Relations 245
B.2 Linear Piezoelectric Equations of State for Hexagonal Crystallographic Class 6mm 246
Appendix C — Solution in Cylindrical Coordinates 249
C.1 General Relations 249
C.2 Linear Piezoelectric Equations of State for Hexagonal Crystallographic Class 6mm 250
C.3 Two-Dimensional Formulation for Plane Stress and Plane Strain 252
Appendix D — Piezoelectric resonators 256
Index 261

Produkt-Details

• Erscheint lt. Verlag: 24.10.2016
• Reihe/Serie: Topics in Mining, Metallurgy and Materials Engineering
• Reihe/Serie: Topics in Mining, Metallurgy and Materials Engineering
• Zusatzinfo: XVII, 251 p. 111 illus., 43 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Logistik / Produktion
• Schlagworte: ceramics manufacturing • ceramic transformer • Equivalent circuit model • higher order theory • material tensor measurement • Piezoelectric transformers
• ISBN-10: 3-319-42481-5 / 3319424815
• ISBN-13: 978-3-319-42481-1 / 9783319424811