The book describes the application of piezoelectric materials, e.g. piezoceramics, in the wide field of actuators and sensors. It gives a step-by-step introduction into the structure and mechanics of piezoelectric beam bending actuators in multilayer technology, which are of increasing importance for industrial applications. The dynamic behaviour of piezoelectric multilayer beam benders is described on the basis of the powerful Lagrangian formalism and Hamiltons principle. Then follows a systematic development of the electromechanical circuit representation for any kind of piezoelectric beam bending actuators within the framework of the electrical network theory. Two different sensor-actuator systems based on a capacitive and an inductive sensor principle are presented and discussed in detail. Analytical simulations of the static and dynamic behaviour are compared to real measurement results of a specially developed piezoelectric multilayer beam bender. Here the suitability of the developed theoretical aspects is shown in an outstanding way.
Author(s): Rudiger Ballas
Edition: 1
Year: 2007
Language: English
Pages: 367
3540326413......Page 1
Microtechnology and MEMS......Page 3
Piezoelectric Multilayer
Beam Bending Actuators......Page 4
Preface......Page 7
Contents......Page 9
List of Symbols......Page 15
Part I
Focus of the Book......Page 24
1
Introduction......Page 25
Part II
Theoretical Aspects and Closed Form Analysis......Page 36
2
Piezoelectric Materials......Page 37
3
Linear Theory of Piezoelectric Materials......Page 51
4
Theory of the Static Behavior of Piezoelectric
Beam Bending Actuators......Page 66
5
Piezoelectric Beam Bending Actuators and
Hamilton’s Principle......Page 96
6
Theory of the Dynamic Behavior of
Piezoelectric Beam Bending Actuators......Page 122
7
Network Representation of Piezoelectric
Multilayered Bending Actuators......Page 142
Part III
Measurement Setup and Validation of
Theoretical Aspects......Page 179
8
Measurement Setup for Piezoelectric Beam
Bending Actuators......Page 180
9
Measurements and Analytical Calculations......Page 189
Part IV
Sensor Integration for Tip Deflection
Measurements......Page 213
10
Piezoelectric Beam Bending Actuator with
Integrated Sensor......Page 214
11
Tip Deflection Measurement - Capacitive
Sensor Principle......Page 218
12
Tip Deflection Measurement - Inductive Sensor
Principle......Page 232
13
Conclusion......Page 264
Part V
Appendix......Page 270
A
Work Done by Stresses Acting on an
Infinitesimal Volume Element......Page 271
B
Derivation of the Coupling Matrix Elements......Page 274
C
Mechanical Potential and Kinetic Energy......Page 291
D
Derivation of the Electrical Enthalpy......Page 293
E
Correlation Between Material Parameters......Page 295
F
Work Done by Extensive Dynamic Quantities......Page 297
G
On the Variation of the Lagrange Function......Page 301
H
On the Variation of the Work Done by
Extensive Quantities......Page 306
I
On the Excitation by a Periodic Force......Page 308
J Particular Solution of the Diffrential Equation for Flexural Vibrations......Page 310
K
Transition to the Diffrential Equations in
Complex Form......Page 312
L
Orthogonality of Di
