Analysis of piezoelectric devices

Jiashi Yang9812568611, 9789812568618

This is the most systematic, comprehensive and up-to-date book on the theoretical analysis of piezoelectric devices. It is a natural continuation of the author s two previous books: An Introduction to the Theory of Piezoelectricity (Springer, 2005) and The Mechanics of Piezoelectric Structures (World Scientific, 2006). Based on the linear, nonlinear, three-dimensional and lower-dimensional structural theories of electromechanical materials, theoretical results are presented for devices such as piezoelectric resonators, acoustic wave sensors, and piezoelectric transducers. The book reflects the contribution to the field from Mindlin s school of applied mechanics researchers since the 1950s.
Contents: Three-Dimensional Theories; Thickness-Shear Modes of Plate Resonators; Slowly Varying Thickness-Shear Modes; Mass Sensors; Fluid Sensors; Gyroscopes — Frequency Effect; Gyroscopes — Charge Effect; Acceleration Sensitivity; Pressure Sensors; Temperature Sensors; Piezoelectric Generators; Piezoelectric Transformers; Power Transmission Through an Elastic Wall; Acoustic Wave Amplifiers.

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Table of contents :
Contents……Page 8
Preface……Page 6
1.1 Nonlinear Electroelasticity for Strong Fields……Page 17
1.2 Linear Piezoelectricity for Infinitesimal Fields……Page 22
1.3 Linear Theory for Small Fields Superposed on a Finite Bias……Page 32
1.4 Cubic Theory for Weak Nonlinearity……Page 38
2.1 Static Thickness-Shear Deformation……Page 41
2.2 Nonlinear Thickness-Shear Deformation……Page 47
2.3 Effects of Initial Fields on Thickness-Shear Deformation……Page 52
2.4 Linear Thickness-Shear Vibration……Page 59
2.5 Effects of Electrode Inertia……Page 65
2.6 Inertial Effects of Imperfectly Bounded Electrodes……Page 68
2.7 Effects of Electrode Inertia and Shear Stiffness……Page 76
2.8 Nonlinear Thickness-Shear Vibration……Page 82
2.9 Effects of Initial Fields on Thickness-Shear Vibration……Page 86
3.1 Exact Waves in a Plate……Page 89
3.2 An Approximate Equation for Thickness-Shear Waves……Page 103
3.3 Thickness-Shear Vibration of Finite Plates……Page 107
3.4 Energy Trapping in Mesa Resonators……Page 109
3.5 Contoured Resonators……Page 113
3.6 Energy Trapping due to Material Inhomogeneity……Page 114
3.7 Energy Trapping by Electrode Mass……Page 119
3.8 Effects of Non-uniform Electrodes……Page 120
3.9 Effects of Electromechanical Coupling on Energy Trapping……Page 122
3.10 Coupling to Flexure……Page 126
3.11 Coupling to Face-Shear and Flexure……Page 130
3.12 Effects of Middle Surface Curvature……Page 135
4.1 Inertial Effect of a Mass Layer by Perturbation……Page 143
4.2 Thickness-Shear Modes of a Plate……Page 147
4.3 Anti-Plane Modes of a Wedge……Page 148
4.4 Torsional Modes of a Conical Shell……Page 150
4.5 Effects of Inertia and Stiffness of a Mass Layer by Perturbation……Page 151
4.6 Effects of Inertia and Stiffness of a Mass Layer by Variation……Page 155
4.7 Radial Modes of a Ring……Page 159
4.8 Effects of Shear Deformability of a Mass Layer……Page 162
4.9 Thickness-Shear Modes of a Plate with Thick Mass Layers……Page 169
4.10 An Ill-Posed Problem in Elasticity for Mass Sensors……Page 173
4.11 Thickness-Shear Modes of a Circular Cylinder……Page 176
4.12 Mass Sensitivity of Surface Waves……Page 179
4.13 Thickness-Twist Waves in a Ceramic Plate……Page 183
4.14 Bechmann’s Number for Thickness-Twist Waves……Page 187
4.15 Thickness-Twist Waves in a Quartz Plate……Page 191
5.1 An Ill-Posed Problem in Elasticity for Fluid Sensors……Page 197
5.2 Perturbation Analysis……Page 203
5.3 Thickness-Shear Modes of a Plate……Page 207
5.4 Torsional Modes of a Cylindrical Shell……Page 208
5.5 Thickness-Shear Modes of a Circular Cylinder……Page 212
5.6 Surface Wave Fluid Sensors……Page 215
5.7 Thickness-Twist Waves in a Ceramic Plate……Page 220
6.1 High Frequency Vibrations of a Small Rotating Piezoelectric Body……Page 225
6.2 Propagation of Plane Waves……Page 226
6.3 Thickness Vibrations of Plates……Page 237
6.4 Propagating Waves in a Rotating Piezoelectric Plate……Page 244
6.5 Surface Waves over a Rotating Piezoelectric Half-Space……Page 252
7.1 A Rectangular Beam……Page 261
7.2 A Circular Tube……Page 274
7.3 A Beam Bimorph……Page 280
7.4 An Inhomogeneous Shell……Page 290
7.5 A Ceramic Ring……Page 298
7.6 A Concentrated Mass and Ceramic Rods……Page 304
7.7 A Ceramic Plate by Two-Dimensional Equations……Page 307
7.8 A Ceramic Plate by Zero-Dimensional Equations……Page 312
8.1 Deformation of a Quartz Plate under Normal Acceleration……Page 317
8.2 First-Order Acceleration Sensitivity……Page 327
8.3 An Estimate of Second-Order Acceleration Sensitivity and its Reduction……Page 329
8.4 Second-Order Perturbation Analysis……Page 334
8.5 Second-Order Normal Acceleration Sensitivity……Page 340
8.6 Effects of Middle Surface Curvature……Page 345
8.7 Vibration Sensitivity……Page 350
9.1 A Rectangular Plate in a Circular Cylindrical Shell……Page 357
9.2 A Circular Plate in a Circular Cylindrical Shell……Page 363
9.3 A Rectangular Plate in a Shallow Shell……Page 368
9.4 A Bimorph……Page 371
9.5 Surface Wave Pressure Sensors Based on Extension……Page 377
9.6 Surface Wave Pressure Sensors Based on Flexure……Page 380
10.1 Thermoelectroelasticity……Page 387
10.2 Linear Theory……Page 390
10.3 Small Fields Superposed on a Thermal Bias……Page 392
10.4 Thickness-Shear Modes of a Free Plate……Page 395
10.5 Thickness-Shear Modes of a Constrained Plate……Page 398
11.1 Thickness-Stretch of a Ceramic Plate……Page 403
11.2 A Circular Shell……Page 411
11.3 A Beam Bimorph……Page 415
11.4 A Spiral Bimorph……Page 423
11.5 Nonlinear Behavior near Resonance……Page 425
12.1 A Thickness-Stretch Mode Plate Transformer……Page 433
12.2 Rosen Transformer……Page 441
12.3 A Thickness-Shear Mode Transformer – Free Vibration……Page 450
12.4 A Thickness-Shear Mode Transformer – Forced Vibration……Page 460
13.1 Formulation of the Problem……Page 467
13.2 Theoretical Analysis……Page 470
13.3 Numerical Results……Page 473
14.1 Equations for Piezoelectric Semiconductors……Page 479
14.2 Equations for a Thin Film……Page 480
14.3 Surface Waves……Page 482
14.4 Interface Waves……Page 490
14.5 Waves in a Plate……Page 494
14.6 Gap Waves……Page 500
References……Page 507
Appendix 1 Notation……Page 517
Appendix 2 Electroelastic Material Constants……Page 519
Index……Page 533