Kaltenbacher Numerical Simulation of Mechatronic Sensors and Actuators

2. Auflage 2007
ISBN: 978-3-540-71360-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 428 Seiten

This is the second, enhanced and updated edition of an essential text for students of mechatronics. It covers both the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. New material includes a section discussing locking effects as occurring in the numerical computation of thin mechanical structures as well as a new chapter on computational aeroacoustics to study the complex phenomenon of flow induced noise.

Autoren/Hrsg.

Kaltenbacher, Manfred

Inhaltsverzeichnis

1;Preface to the second edition;5
1.1;Acknowledgment;6
2;Preface to the first edition;7
2.1;Acknowledgements;10
3;Notation;11
3.1;Mathematical symbols Finite Element Method;11
3.2;Acoustics;12
3.3;Electromagnetics;12
3.4;Mechanics;12
4;Contents;13
5;1 Introduction;19
6;2 The Finite Element (FE) Method;25
6.1;2.1 Finite Element Formulation;27
6.2;2.2 Finite Element Method for a 1D Problem;31
6.3;2.3 Nodal (Lagrangian) Finite Elements;38
6.4;2.4 Finite Element Procedure;50
6.5;2.5 Time Discretization;53
6.6;2.6 Integration over Surfaces;61
6.7;2.7 Edge (N´ ed ´ elec) Finite Elements;61
6.8;2.8 Discretization Error;63
7;3 Mechanical Field;68
7.1;3.1 Navier’s Equation;68
7.2;3.2 Deformation and Displacement Gradient;72
7.3;3.3 Mechanical Strain;73
7.4;3.4 Constitutive Equations;77
7.5;3.5 Waves in Solid Bodies;80
7.6;3.6 Material Properties;82
7.7;3.7 Numerical Computation;83
7.8;3.8 Locking and Efficient Solution Approaches;95
8;4 Electromagnetic Field;110
8.1;4.1 Maxwell’s Equations;110
8.2;4.2 Quasistatic Electromagnetic Fields;118
8.3;4.3 Electrostatic Field;121
8.4;4.4 Material Properties;121
8.5;4.5 Electromagnetic Interface Conditions;126
8.6;4.6 Numerical Computation: Electrostatics;130
8.7;4.7 Numerical Computation: Electromagnetics;131
8.8;4.8 Numerical Examples;152
9;5 Acoustic Field;155
9.1;5.1 Wave Theory of Sound;155
9.2;5.2 Quantitative Measure of Sound;167
9.3;5.3 Non-linear Acoustic Wave Equation;172
9.4;5.4 Numerical Computation;176
9.5;5.5 Treatment of Open Domain Problems;189
9.6;5.6 Numerical Examples;200
10;6 Coupled Electrostatic-Mechanical Systems;211
10.1;6.1 Electrostatic Force;212
10.2;6.2 Numerical Computation;218
11;7 Coupled Magnetomechanical Systems;223
11.1;7.1 General Moving/Deforming Body;223
11.2;7.2 Electromagnetic Force;225
11.3;7.3 Numerical Computation;227
12;8 Coupled Mechanical-Acoustic Systems;244
12.1;8.1 Solid–Fluid Interface;245
12.2;8.2 Coupled Field Formulation;246
12.3;8.3 Numerical Computation;248
13;9 Piezoelectric Systems;257
13.1;9.1 Constitutive Equation;257
13.2;9.2 Governing Equations;258
13.3;9.3 Piezoelectric Material Properties;259
13.4;9.4 Models for Non-linear Piezoelectricity;263
13.5;9.5 Hysteresis Model;267
13.6;9.6 Numerical Computation;271
13.7;9.7 Numerical Examples;275
14;10 Computational Aeroacoustics;281
14.1;10.1 Requirements for Numerical Schemes;281
14.2;10.2 Lighthill’s Analogy and its Extension;284
14.3;10.3 Finite Element Formulation;289
14.4;10.4 Validation: Co-Rotating Vortex Pair;293
15;11 Algebraic Solvers;297
15.1;11.1 Preconditioned Conjugate Gradient (PCG) Method;297
15.2;11.2 Multigrid (MG) Method;299
15.3;11.3 Geometric MG Method;301
15.4;11.4 Algebraic MG Method;307
16;12 Industrial Applications;326
16.1;12.1 Electrodynamic Loudspeaker;326
16.2;12.2 Noise Computation of Power Transformers;333
16.3;12.3 Fast-switching Electromagnetic Valves;343
16.4;12.4 Cofired Piezoceramic Multilayer Actuators;353
16.5;12.5 Capacitive Micromachined Ultrasound Transducers;358
16.6;12.6 High-Intensity Focused Ultrasound;370
16.7;12.7 Noise Generated from a Flow around a Square Cylinder;379
17;A Norms;394
17.1;A.1 Vector Norms;394
17.2;A.2 Matrix Norms;395
18;B Scalar and Vector Fields;396
18.1;B.1 The Nabla (.) Operator;399
18.2;B.2 Definition of Gradient, Divergence, and Curl;399
18.3;B.3 The Gradient;400
18.4;B.4 The Flux;402
18.5;B.5 Divergence;403
18.6;B.6 Divergence Theorem (Gauss Theorem);405
18.7;B.7 The Circulation;405
18.8;B.8 The Curl;406
18.9;B.9 Stoke’s Theorem;408
18.10;B.10 Green’s Integral Theorems;409
18.11;B.11 Application of the Operators;410
18.12;B.12 Irrotational Vector Fields;410
18.13;B.13 Solenoidal Vector Fields;411
19;C Appropriate Function Spaces;412
20;D Solution of Nonlinear Equations;417
20.1;D.1 Fixed-point Iteration;419
20.2;D.2 Newton’s Method;420
21;References;423
22;Index;435