An introduction to the theory of piezoelectricity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2005
|
| Schriftenreihe: | Advances in mechanics and mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. [277]-280) and index |
| Beschreibung: | xiv, 299 p. ill. |
| ISBN: | 0387235736 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to the theory of piezoelectricity |c by Jiashi Yang |
| 264 | 1 | |a New York |b Springer |c 2005 | |
| 300 | |a xiv, 299 p. |b ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Advances in mechanics and mathematics |v 9 | |
| 500 | |a Includes bibliographical references (p. [277]-280) and index | ||
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| 650 | 4 | |a Linear operators |v Textbooks | |
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Datensatz im Suchindex
| _version_ | 1804133539707355136 |
|---|---|
| adam_text | Contents
Foreword xi
Preface xiii
1 1
CHAPTER ONE 1
NONLINEAR ELECTROELASTICITY FOR STRONG FIELDS 1
1. DEFORMATION AND MOTION OF A CONTINUUM 1
2. GLOBAL BALANCE LAWS 9
2.1 Polarization 10
2.2 Piezoelectric Effects 10
2.3 Electric Body Force, Couple, and Power 11
2.4 Balance Laws 12
3. LOCAL BALANCE LAWS 13
4. MATERIAL FORM OF LOCAL BALANCE LAWS 18
5. CONSTITUTIVE RELATIONS 21
6. INITIAL BOUNDARY VALUE PROBLEM 24
7. VARIATIONAL FORMULATION 26
8. TOTAL STRESS FORMULATION 28
2 31
CHAPTER TWO 31
LINEAR PIEZOELECTRICITY FOR INFINITESIMAL FIELDS 31
1. LINEARIZATION 31
2. BOUNDARY VALUE PROBLEM 35
2.1 Displacement Potential Formulation 35
2.2 Boundary Value Problem 35
2.3 Principle of Superposition 37
2.4 Compatibility 38
3. VARIATIONAL PRINCIPLES 39
3.1 Hamilton s Principle 39
3.2 Mixed Variational Principles 40
3.3 Conservation Laws 41
4. UNIQUENESS 42
4.1 Poynting s Theorem 42
4.2 Energy Integral 43
vi
4.3 Uniqueness 43
5. OTHER FORMULATIONS 44
5.1 Four Vector Formulation 44
5.2 Vector Potential Formulation 45
6. CURVILINEAR COORDINATES 46
6.1 Cylindrical Coordinates 46
6.2 Spherical Coordinates 47
7. COMPACT MATRIX NOTATION 48
8. POLARIZED CERAMICS 50
9. QUARTZ AND LANGASITE 53
10. LITHIUM NIOBATE AND LITHIUM TANTALATE 57
t 59
CHAPTER THREE 59
STATIC PROBLEMS 59
1. EXTENSION OF A CERAMIC ROD 59
1.1 Boundary Value Problem 60
1.2 Shorted Electrodes 61
1.3 Open Electrodes 61
1.4 Electromechanical Coupling Factor 61
2. THICKNESS STRETCH OF A CERAMIC PLATE 62
2.1 Boundary Value Problem 63
2.2 Shorted Electrodes 64
2.3 Open Electrodes 64
2.4 Electromechanical Coupling Factor 64
3. THICKNESS SHEAR OF A QUARTZ PLATE 65
3.1 Boundary Value Problem 65
3.2 Free Surfaces 66
3.3 Clamped Surfaces 67
3.4 Electromechanical Coupling Factor 68
4. TORSION OF A CERAMIC CIRCULAR CYLINDER 68
1.1 Boundary Value Problem 69
1.2 Shorted Electrodes 70
1.3 Open Electrodes 70
5. TANGENTIAL THICKNESS SHEAR OF A
CERAMIC CIRCULAR CYLINDER 71
6. ANTI PLANE PROBLEMS OF POLARIZED CERAMICS 72
7. A SURFACE DISTRIBUTION OF ELECTRIC POTENTIAL 74
8. A CIRCULAR HOLE UNDER AXISYMMETRIC LOADS 75
9. AXIAL THICKNESS SHEAR OF A CIRCULAR CYLINDER....78
10. A CIRCULAR HOLE UNDER SHEAR 79
11. A CIRCULAR CYLINDER IN AN ELECTRIC FIELD 82
vii
12. A SCREW DISLOCATION 85
13. A CRACK 86
4 89
CHAPTER FOUR 89
VIBRATIONS OF FINITE BODIES 89
1. THICKNESS STRETCH VIBRATION OF A CERAMIC
PLATE (THICKNESS EXCITATION) 89
1.1 Boundary Value Problem 90
1.2 Free Vibration 91
1.3 Forced Vibration 92
2. THICKNESS STRETCH VIBRATION OF A CERAMIC
PLATE (LATERAL EXCITATION) 94
2.1 Boundary Value Problem 94
2.2 Free Vibration 96
2.3 Forced Vibration 96
3. THICKNESS SHEAR VIBRATION OF A QUARTZ
PLATE (THICKNESS EXCITATION) 97
3.1 Boundary Value Problem 97
3.2 Free Vibration 99
3.3 Forced Vibration 101
3.4 Mechanical Effects of Electrodes 101
4. TANGENTIAL THICKNESS SHEAR VIBRATION OF
A CIRCULAR CYLINDER 105
5. AXIAL THICKNESS SHEAR VIBRATION OF A
CIRCULAR CYLINDER 108
5.1 Boundary Value Problem 109
5.2 Clamped and Electroded Surfaces 110
5.3 Free andUnelectrodedSurfaces Ill
5.4 Free and Electroded Surfaces Ill
6. SOME GENERAL RESULTS 112
6.1 Abstract Formulation 113
6.2 Self Adjointness 113
6.3 Reality 114
6.4 Orthogonality 115
6.5 Positivity 115
6.6 Variational Formulation 116
6.7 Perturbation Based on Variational Formulation 117
6.8 Perturbation Based on Abstract Formulation 118
7. EXTENSIONAL VIBRATION OF A THIN ROD 119
8. RADIAL VIBRATION OF A THIN RING 121
9. RADIAL VIBRATION OF A THIN PLATE 122
viii
10. RADIAL VIBRATION OF A THIN CYLINDRICAL SHELL...126
11. RADIAL VIBRATION OF A THIN SPHERICAL SHELL 127
12. FREQUENCY SHIFTS DUE TO SURFACE
ADDITIONAL MASS 129
5 135
CHAPTER FIVE 135
WAVES IN UNBOUNDED REGIONS 135
1. PLANE WAVES 135
2. REFLECTION AND REFRACTION 137
2.1 Reflection 137
2.2 Reflection and Refraction 139
3. SURFACE WAVES 141
3.1 A Half Space with an Electroded Surface 143
3.2 A Half Space with an Unelectroded Surface 144
4. INTERFACE WAVES 145
4.1 An Electroded Interface 146
4.2 An Unelectroded Interface 147
5. WAVES IN A PLATE 147
5.1 Anti Symmetric Waves 148
5.2 Symmetric Waves 149
6. WAVES IN A PLATE ON A SUBSTRATE 151
7. GAP WAVES 154
7.1 A Gap between Two Half Spaces of Different Ceramics 154
7.2 A Gap between Two Half Spaces of the Same Ceramic 157
8. WAVES ON A CIRCULAR CYLINDRICAL SURFACE 160
9. ACOUSTIC WAVE GENERATION 163
, 167
CHAPTER SIX 167
LINEAR EQUATIONS FOR SMALL FIELDS SUPERPOSED
ON FINITE BIASING FIELDS 167
1. A NONLINEAR SPRING 167
2. LINEARIZATION ABOUT A BIAS 169
2.1 Linearization of Differential Equations 171
2.2 A Variational Principle 174
2.3 Linearization Using the Total Stress Formulation 174
3. VARIATIONAL APPROACH 175
4. SMALL BIASING FIELDS 178
5. THEORY OF INITIAL STRESS 179
6. FREQUENCY PERTURBATION 180
ix
7. ELECTROSTRICTIVE CERAMICS 184
7.1 Nonlinear Theory 184
7.2 Effects of a Small, Electrical Bias 185
7 187
CHAPTER SEVEN 187
CUBIC AND OTHER EFFECTS 187
1. CUBIC THEORY 187
1.1 Cubic Effects 187
1.2 Quadratic Effects 189
2. NONLOCAL EFFECTS 190
2.1 Nonlocal Theory 190
2.2 Thin Film Capacitance 190
3. GRADIENT EFFECTS 196
3.1 Gradient Effect as a Weak Nonlocal Effect 196
3.2 Gradient Effect and Lattice Dynamics 197
3.3 Polarization Gradient 198
3.4 Electric Field Gradient and Electric Quadrupole 198
4. THERMAL AND VISCOUS EFFECTS 206
4.1 Equations in Spatial Form 206
4.2 Equations in Material Form 207
4.3 Constitutive Equations 208
4.4 Boundary Value Problem 209
4.5 Linear Equations 209
5. SEMICONDUCTOR 212
5.1 Governing Equations 212
5.2 Surface Waves 213
6. DYNAMIC THEORY 221
6.1 Governing Equations 221
6.2 Quasistatic Approximation 222
6.3 Anti Plane Problems of Ceramics 223
6.4 Surface Waves 225
6.5 Electromagnetic Radiation 228
8 235
CHAPTER EIGHT 235
PIEZOELECTRIC DEVICES 235
1. GYROSCOPES 235
1.1 Governing Equations 236
1.2 An Example 236
X
2. TRANSFORMERS 242
2.1 A One Dimensional Model 242
2.2 Free Vibration Analysis 246
2.3 Forced Vibration Analysis 247
2.4 Numerical Results 250
3. PRESSURE SENSORS 254
4. TEMPERATURE SENSORS 260
4.1 Equations for Small Fields Superposed on a Thermal Bias....261
4.2 Analysis of a Temperature Sensor 264
5. VIBRATION SENSITIVITY OF A RESONATOR 269
REFERENCES 277
Index 281
Appendix 1 List of Notation 285
Appendix 2 Electroelastic Material Constants 287
|
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| id | DE-604.BV019992762 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:20Z |
| institution | BVB |
| isbn | 0387235736 |
| language | English |
| lccn | 2005040502 |
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| series | Advances in mechanics and mathematics |
| series2 | Advances in mechanics and mathematics |
| spelling | Yang, Jiashi Verfasser aut An introduction to the theory of piezoelectricity by Jiashi Yang New York Springer 2005 xiv, 299 p. ill. txt rdacontent n rdamedia nc rdacarrier Advances in mechanics and mathematics 9 Includes bibliographical references (p. [277]-280) and index Piezoelectricity Textbooks Linear operators Textbooks Festkörper (DE-588)4016918-2 gnd rswk-swf Elektroelastizität (DE-588)4334473-2 gnd rswk-swf Piezoelektrizität (DE-588)4322722-3 gnd rswk-swf Piezoelektrizität (DE-588)4322722-3 s DE-604 Festkörper (DE-588)4016918-2 s Elektroelastizität (DE-588)4334473-2 s 1\p DE-604 Advances in mechanics and mathematics 9 (DE-604)BV017903734 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013314623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yang, Jiashi An introduction to the theory of piezoelectricity Advances in mechanics and mathematics Piezoelectricity Textbooks Linear operators Textbooks Festkörper (DE-588)4016918-2 gnd Elektroelastizität (DE-588)4334473-2 gnd Piezoelektrizität (DE-588)4322722-3 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4334473-2 (DE-588)4322722-3 |
| title | An introduction to the theory of piezoelectricity |
| title_auth | An introduction to the theory of piezoelectricity |
| title_exact_search | An introduction to the theory of piezoelectricity |
| title_full | An introduction to the theory of piezoelectricity by Jiashi Yang |
| title_fullStr | An introduction to the theory of piezoelectricity by Jiashi Yang |
| title_full_unstemmed | An introduction to the theory of piezoelectricity by Jiashi Yang |
| title_short | An introduction to the theory of piezoelectricity |
| title_sort | an introduction to the theory of piezoelectricity |
| topic | Piezoelectricity Textbooks Linear operators Textbooks Festkörper (DE-588)4016918-2 gnd Elektroelastizität (DE-588)4334473-2 gnd Piezoelektrizität (DE-588)4322722-3 gnd |
| topic_facet | Piezoelectricity Textbooks Linear operators Textbooks Festkörper Elektroelastizität Piezoelektrizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013314623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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