The mechanics of piezoelectric structures

Jiashi Yang9812567011, 9789812567017

A continuation of the author’s previous book “An Introduction to the Theory of Piezoelectricity” (Springer, New York, 2005) on the three-dimensional theory of piezoelectricity, this volume covers lower dimensional theories for various piezoelectric structures and device applications. The development of two-, one- and zero-dimensional theories for high frequency vibrations of piezoelectric plates, shells, beams, rings curved bars and parallelepipeds is systematically presented. In addition to linear piezoelectricity, certain nonlinear effects are also considered and examples for device applications are provided. The material emphasizes dynamic theories and high frequency motions as well as device applications as there are relatively few books on piezoelectric structures, especially for high frequency theories. The volume is destined to be one of the most systematic and comprehensive books on piezoelectric structures.

---

Table of contents :
Contents……Page 10
Preface……Page 6
1.1 Nonlinear Electroelasticity for Strong Fields……Page 14
1.2 Linear Piezoelectricity for Weak Fields……Page 20
1.3 Linear Theory for Small Fields Superposed on a Finite Bias……Page 25
1.4 Cubic Theory for Weak Nonlinearity……Page 32
2.1 Exact Modes in a Plate……Page 35
2.2 Power Series Expansion……Page 47
2.3 Zero-Order Theory for Extension……Page 54
2.4 First-Order Theory……Page 71
2.5 Second-Order Theory……Page 120
3.1 Elastic Plates with Symmetric Piezoelectric Actuators……Page 135
3.2 Elastic Plates with Piezoelectric Actuators on One Side……Page 146
3.3 Laminated Piezoelectric Plates……Page 158
3.4 A Plate on a Substrate……Page 163
4.1 Plates under Biasing Fields……Page 181
4.2 Large Thickness-Shear Deformations……Page 192
5.1 First-Order Theory……Page 202
5.2 Classical Theory……Page 209
5.3 Membrane Theory……Page 212
5.4 Vibration of Ceramic Shells……Page 214
5.5 A Shell on a Non-Thin Body……Page 217
6.1 Power Series Expansion……Page 238
6.2 Zero-Order Theory For Extension……Page 240
6.3 First-Order Theory……Page 248
7.1 First-Order Theory……Page 275
7.2 Classical Theory……Page 279
7.3 Radial Vibration of a Ceramic Ring……Page 281
8.1 Power Series Expansion……Page 283
8.2 Zero-Order Equations……Page 286
8.3 A Piezoelectric Gyroscope……Page 287
8.4 A Transformer – Forced Vibration Analysis……Page 296
References……Page 304
Appendix 1 Notation……Page 309
Appendix 2 Electroelastic Material Constants……Page 311
Index……Page 325