Karnovsky / Lebed Theory of Vibration Protection

1. Auflage 2016
ISBN: 978-3-319-28020-2
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 708 Seiten

This text is an advancement of the theory of vibration protection of mechanical systems with lumped and distributed parameters.  The book offers various concepts and methods of solving vibration protection problems, discusses the advantages and disadvantages of different methods, and the fields of their effective applications. Fundamental approaches of vibration protection, which are considered in this book, are the passive, parametric and optimal active vibration protection. The passive vibration protection is based on vibration isolation, vibration damping and dynamic absorbers. Parametric vibration protection theory is based on the Shchipanov-Luzin invariance principle.  Optimal active vibration protection theory is based on the Pontryagin principle and the Krein moment method.The book also contains special topics such as suppression of vibrations at the source of their occurrence and the harmful influence of vibrations on humans.< Numerous examples, which illustrate the theoretical ideas of each chapter, are included.This book is intended for graduate students and engineers. It is assumed that a reader has working knowledge of theory of vibrations, differential equations, andcomplex analysis.About the Authors.Igor A Karnovsky, Ph.D., Dr. Sci., is a specialist in structural analysis, theory of vibration and optimal control of vibration. He has 40 years  of experience in research, teaching and consulting in this field, and is the author of more than 70 published scientific papers, including two books in Structural Analysis (published with Springer in 2010-2012) and three handbooks in Structural Dynamics (published with McGraw Hill in 2001-2004). He also holds a number of vibration-control-related patents.Evgeniy Lebed, Ph.D., is a specialist in applied mathematics and engineering. He has 10 years of experience in research, teaching and consulting in this field. The main sphere of his research interests are qualitative theory of differential equations, integral transforms and frequency-domain analysis with application to image and signal processing. He is the author of 15 published scientific papers and a US patent (2015).

Igor A Karnovsky, Ph.D., Dr. Sci., is a specialist in structural analysis, theory of vibration and optimal control of vibration. He has 40 years  of experience in research, teaching and consulting in this field, and is the author of more than 70 published scientific papers, including two books in Structural Analysis (published with Springer in 2010-2012) and three handbooks in Structural Dynamics (published with McGraw Hill in 2001-2004). He also holds a number of vibration-control-related patents.
Evgeniy Lebed, Ph.D., is a specialist in applied mathematics and engineering. He has 10 years of experience in research, teaching and consulting in this field. The main sphere of his research interests are qualitative theory of differential equations, integral transforms and frequency-domain analysis with application to image and signal processing. He is the author of 15 published scientific papers and a US patent (2015).

Autoren/Hrsg.

Karnovsky, Igor A.

Lebed, Evgeniy

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgments;10
3;Contents;12
4;About the Authors;22
5;Introduction;24
5.1;Mechanical Exposure and Vibration Protection Methods;24
5.1.1;Source of Vibration and Vibration Protection Objects;24
5.1.2;Mechanical Exposures and Their Influence on Technical Objects and Humans;27
5.1.2.1;Linear Overload;27
5.1.2.2;Vibrational Exposure;28
5.1.2.3;Impact Exposure;30
5.1.2.4;Influence of Mechanical Exposure on Technical Objects and Humans;30
5.1.3;Dynamical Models of Vibration Protection Objects;31
5.1.4;Vibration Protection Methods;35
5.1.5;Estimating the Effectiveness of Vibration Reduction;37
5.1.6;Frequency Spectrum: Linear, Log, and Decibel Units;38
6;Part I: Passive Vibration Protection;47
6.1;Chapter 1: Vibration Isolation of a System with One or More Degrees of Freedom;48
6.1.1;1.1 Design Diagrams of Vibration Protection Systems;48
6.1.2;1.2 Linear Viscously Damped System. Harmonic Excitation and Vibration Protection Criteria;50
6.1.2.1;1.2.1 Simplest Mechanical Model of a Vibration Protection System;51
6.1.2.2;1.2.2 Force Excitation. Dynamic and Transmissibility Coefficients;51
6.1.2.3;1.2.3 Kinematic Excitation. Overload Vibration Coefficient and Estimation of Relative Displacement;55
6.1.3;1.3 Complex Amplitude Method;60
6.1.3.1;1.3.1 Vector Representation of Harmonic Quantities;60
6.1.3.2;1.3.2 Single-Axis Vibration Isolator;62
6.1.3.3;1.3.3 Argand Diagram;64
6.1.3.4;1.3.4 System with Two Degrees of Freedom;65
6.1.4;1.4 Linear Single-Axis Vibration Protection Systems;66
6.1.4.1;1.4.1 Damper with Elastic Suspension. Transmissibility Coefficient;67
6.1.4.2;1.4.2 Simplification of Vibration Isolators;69
6.1.4.3;1.4.3 Vibration Isolators Which Cannot Be Simplified;71
6.1.4.4;1.4.4 Special Types of Vibration Isolators;71
6.1.5;1.5 Vibration Protection System of Quasi-Zero Stiffness;73
6.1.6;References;80
6.2;Chapter 2: Mechanical Two-Terminal Networks for a System with Lumped Parameters;82
6.2.1;2.1 Electro-Mechanical Analogies and Dual Circuits;82
6.2.2;2.2 Principal Concepts of Mechanical Networks;87
6.2.2.1;2.2.1 Vector Representation of Harmonic Force;87
6.2.2.2;2.2.2 Kinematic Characteristics of Motion;87
6.2.2.3;2.2.3 Impedance and Mobility of Passive Elements;88
6.2.3;2.3 Construction of Two-Terminal Networks;93
6.2.3.1;2.3.1 Two-Terminal Network for a Simple Vibration Isolator;94
6.2.3.2;2.3.2 Two-Cascade Vibration Protection System;97
6.2.3.3;2.3.3 Complex Dynamical System and Its Coplanar Network;98
6.2.4;2.4 Mechanical Network Theorems;100
6.2.4.1;2.4.1 Combination of Mechanical Elements;101
6.2.4.2;2.4.2 Kirchhoff´s Laws;103
6.2.4.3;2.4.3 Reciprocity Theorem;104
6.2.4.4;2.4.4 Superposition Principle;104
6.2.5;2.5 Simplest One-Side m-k-b Vibration Isolator;105
6.2.5.1;2.5.1 Force Excitation;105
6.2.5.2;2.5.2 Kinematic Excitation;109
6.2.6;2.6 Complex One-Sided m-k-b Vibration Isolators;111
6.2.6.1;2.6.1 Vibration Isolator with Elastic Suspension;111
6.2.6.2;2.6.2 Two-Cascade Vibration Protection System;112
6.2.7;References;118
6.3;Chapter 3: Mechanical Two-Terminal and Multi-Terminal Networks of Mixed Systems;120
6.3.1;3.1 Fundamental Characteristics of a Deformable System with a Vibration Protection Device;120
6.3.1.1;3.1.1 Input and Transfer Impedance and Mobility;121
6.3.1.2;3.1.2 Impedance and Mobility Relating to an Arbitrary Point;127
6.3.2;3.2 Deformable Support of a Vibration Protection System;129
6.3.2.1;3.2.1 Free Vibrations of Systems with a Finite Number of Degrees of Freedom;129
6.3.2.2;3.2.2 Generalized Model of Support and Its Impedance;134
6.3.2.3;3.2.3 Support Models and Effectiveness Coefficient of Vibration Protection;136
6.3.3;3.3 Optimal Synthesis of the Fundamental Characteristics;138
6.3.3.1;3.3.1 Problem Statement of Optimal Synthesis. Brune´s Function;139
6.3.3.2;3.3.2 Foster´s Canonical Schemes;140
6.3.3.3;3.3.3 Cauer´s Canonical Schemes;145
6.3.3.4;3.3.4 Support as a Deformable System with Distributed Mass;149
6.3.4;3.4 Vibration Protection Device as a Mechanical Four-Terminal Network;155
6.3.4.1;3.4.1 Mechanical Four-Terminal Network for Passive Elements with Lumped Parameters;156
6.3.4.2;3.4.2 Connection of an 4N with Support of Impedance Zf;160
6.3.4.3;3.4.3 Connections of Mechanical Four-Terminal Networks;161
6.3.5;3.5 Mechanical Multi-Terminal Networks for Passive Elements with Distributed Parameters;172
6.3.5.1;3.5.1 M4TN for Longitudinal Vibration of Rod;173
6.3.5.2;3.5.2 Mechanical Eight-Terminal Network for Transversal Vibration of a Uniform Beam;175
6.3.6;3.6 Effectiveness of Vibration Protection;180
6.3.7;References;184
6.4;Chapter 4: Arbitrary Excitation of Dynamical Systems;186
6.4.1;4.1 Transfer Function;186
6.4.1.1;4.1.1 Analysis in the Time Domain;186
6.4.1.2;4.1.2 Logarithmic Plot of Frequency Response. Bode Diagram;193
6.4.2;4.2 Green´s Function and Duhamel´s Integral;196
6.4.2.1;4.2.1 System with Lumped Parameters;197
6.4.2.1.1;4.2.1.1 Force Excitation;197
6.4.2.1.2;4.2.1.2 Kinematic Excitation;200
6.4.2.2;4.2.2 System with Distributed Parameters;201
6.4.3;4.3 Standardizing Function;204
6.4.4;References;210
6.5;Chapter 5: Vibration Damping;211
6.5.1;5.1 Phenomenological Aspects;212
6.5.1.1;5.1.1 Models of Material;212
6.5.1.2;5.1.2 Complex Modulus of Elasticity;214
6.5.1.3;5.1.3 Dissipative Forces;215
6.5.1.4;5.1.4 Dimensionless Parameters of Energy Dissipation;216
6.5.2;5.2 Hysteretic Damping;220
6.5.2.1;5.2.1 Hysteresis Loop;220
6.5.2.2;5.2.2 Hysteretic Damping Concept;222
6.5.2.3;5.2.3 Forced Vibration of a System with One Degree of Freedom;223
6.5.2.4;5.2.4 Comparison of Viscous and Hysteretic Damping;226
6.5.3;5.3 Structural Damping;226
6.5.3.1;5.3.1 General;227
6.5.3.2;5.3.2 Energy Dissipation in Systems with Lumped Friction;229
6.5.3.3;5.3.3 Energy Dissipation in Systems with Distributed Friction;230
6.5.4;5.4 Equivalent Viscous Damping;233
6.5.4.1;5.4.1 Absorption Coefficient;233
6.5.4.2;5.4.2 Equivalent Viscoelastic Model;233
6.5.5;5.5 Vibration of a Beam with Internal Hysteretic Friction;235
6.5.6;5.6 Vibration of a Beam with External Damping Coating;238
6.5.6.1;5.6.1 Vibration-Absorbing Layered Structures;239
6.5.6.2;5.6.2 Transverse Vibration of a Two-Layer Beam;240
6.5.6.2.1;5.6.2.1 Bending of a Composite Beam;240
6.5.6.2.2;5.6.2.2 Coefficient of Loss of a Composite Beam;242
6.5.6.2.3;5.6.2.3 Free and Forced Vibration of a Composite Beam;243
6.5.7;5.7 Aerodynamic Damping;244
6.5.7.1;5.7.1 The Interaction of a Structure with a Flow;245
6.5.7.2;5.7.2 Aerodynamic Reduction of Vibration;246
6.5.8;References;248
6.6;Chapter 6: Vibration Suppression of Systems with Lumped Parameters;250
6.6.1;6.1 Dynamic Absorber;250
6.6.2;6.2 Dynamic Absorbers with Damping;256
6.6.2.1;6.2.1 Absorber with Viscous Damping;257
6.6.2.2;6.2.2 Viscous Shock Absorber;259
6.6.2.3;6.2.3 Absorber with Coulomb Damping;260
6.6.3;6.3 Roller Inertia Absorbers;262
6.6.4;6.4 Absorbers of Torsional Vibration;265
6.6.4.1;6.4.1 Centrifugal Pendulum Vibration Absorber;265
6.6.4.2;6.4.2 Pringle´s Vibration Absorber;269
6.6.5;6.5 Gyroscopic Vibration Absorber;271
6.6.5.1;6.5.1 Elementary Theory of Gyroscopes;272
6.6.5.1.1;6.5.1.1 Free Gyroscope;272
6.6.5.1.2;6.5.1.2 Action of a Force Applied to the Axis of a Gyroscope;272
6.6.5.1.3;6.5.1.3 Regular Precession of a Heavy Gyroscope;273
6.6.5.1.4;6.5.1.4 The Gyroscopic Effect;274
6.6.5.2;6.5.2 Schlick's Gyroscopic Vibration Absorber;275
6.6.6;6.6 Impact Absorbers;277
6.6.6.1;6.6.1 Pendulum Impact Absorber;278
6.6.6.2;6.6.2 Floating Impact Absorber;280
6.6.6.3;6.6.3 Spring Impact Absorber;281
6.6.7;6.7 Autoparametric Vibration Absorber;281
6.6.8;References;285
6.7;Chapter 7: Vibration Suppression of Structures with Distributed Parameters;287
6.7.1;7.1 Krylov-Duncan Method;287
6.7.2;7.2 Lumped Vibration Absorber of the Beam;292
6.7.3;7.3 Distributed Vibration Absorber;296
6.7.4;7.4 Extension Rod as Absorber;299
6.7.5;References;305
6.8;Chapter 8: Parametric Vibration Protection of Linear Systems;306
6.8.1;8.1 General;306
6.8.2;8.2 Invariance Principle;307
6.8.2.1;8.2.1 Shchipanov-Luzin Absolute Invariance;307
6.8.2.2;8.2.2 Invariance up to epsi;309
6.8.3;8.3 Parametric Vibration Protection of the Spinning Rotor;312
6.8.4;8.4 Physical Feasibility of the Invariance Conditions;316
6.8.4.1;8.4.1 Uncontrollability of ``Perturbation-Coordinate´´ Channel;316
6.8.4.2;8.4.2 Petrov´s Two-Channel Principle;318
6.8.4.3;8.4.3 Dynamic Vibration Absorber;319
6.8.5;8.5 Parametric Vibration Protection of the Plate Under a Moving Load;321
6.8.5.1;8.5.1 Mathematical Model of a System;321
6.8.5.2;8.5.2 Petrov´s Principle;325
6.8.6;References;328
6.9;Chapter 9: Nonlinear Theory of Vibration Protection Systems;330
6.9.1;9.1 General;330
6.9.1.1;9.1.1 Types of Nonlinearities and Theirs Characteristics;331
6.9.1.1.1;9.1.1.1 Static Nonlinear Characteristics;331
6.9.1.1.2;9.1.1.2 Dynamic Nonlinear Characteristics;333
6.9.1.2;9.1.2 Features of Nonlinear Vibration;335
6.9.2;9.2 Harmonic Linearization Method;336
6.9.2.1;9.2.1 Method Foundation;336
6.9.2.2;9.2.2 Coefficients of Harmonic Linearization;341
6.9.3;9.3 Harmonic Excitation;344
6.9.3.1;9.3.1 Duffing´s Restoring Force;344
6.9.3.2;9.3.2 Nonlinear Restoring Force and Viscous Damping;348
6.9.3.3;9.3.3 Linear Restoring Force and Coulomb´s Friction;352
6.9.3.4;9.3.4 Internal Friction;357
6.9.4;9.4 Nonlinear Vibration Absorber;360
6.9.5;9.5 Harmonic Linearization and Mechanical Impedance Method;363
6.9.6;9.6 Linearization of a System with an Arbitrary Number of Degrees of Freedom;365
6.9.7;References;370
7;Part II: Active Vibration Protection;372
7.1;Chapter 10: Pontryagin´s Principle;373
7.1.1;10.1 Active Vibration Protection of Mechanical Systems as a Control Problem;373
7.1.1.1;10.1.1 Mathematical Model of Vibration Protection Problem;373
7.1.1.2;10.1.2 Classification of Optimal Vibration Protection Problems;380
7.1.2;10.2 Representation of an Equation of State in Cauchy´s Matrix Form;381
7.1.3;10.3 Qualitative Properties of Vibration Protection Systems;387
7.1.3.1;10.3.1 Accessibility, Controllability, Normality;387
7.1.3.2;10.3.2 Stability;390
7.1.4;10.4 Pontryagin´s Principle;395
7.1.5;10.5 Vibration Suppression of a System with Lumped Parameters;397
7.1.5.1;10.5.1 Vibration Suppression Problems Without Constraints;398
7.1.5.1.1;10.5.1.1 Fixed Terminal Time and Functional of Energy;398
7.1.5.1.2;10.5.1.2 Non-Fixed Terminal Time, Combined Functional of Energy and Time;402
7.1.5.1.3;10.5.1.3 Fixed Time, Combined Functional of Energy and Coordinates;403
7.1.5.1.4;10.5.1.4 General Case: Quadratic Functional and Fixed Time;405
7.1.5.2;10.5.2 Vibration Suppression Problem with Constrained Exposure. Quadratic Functional, Fixed Time and Fixed End;407
7.1.6;10.6 Bushaw´s Minimum-Time Problem;409
7.1.7;10.7 Minimum Isochrones;417
7.1.8;Problems;420
7.1.9;References;423
7.2;Chapter 11: Krein Moments Method;425
7.2.1;11.1 The Optimal Active Vibration Protection Problem as the l-moments Problem;426
7.2.1.1;11.1.1 Formulation of the Problem of Vibration Suppression as a Moment Problem;426
7.2.1.2;11.1.2 The l-moments Problem and Numerical Procedures;431
7.2.2;11.2 Time-Optimal Problem for a Linear Oscillator;433
7.2.2.1;11.2.1 Constraint of Energy;433
7.2.2.2;11.2.2 Control with Magnitude Constraint;435
7.2.3;11.3 Optimal Active Vibration Protection of Continuous Systems;438
7.2.3.1;11.3.1 Truncated Moments Problem;438
7.2.3.2;11.3.2 Vibration Suppression of String. Standardizing Function;438
7.2.3.3;11.3.3 Vibration Suppression of a Beam;444
7.2.3.4;11.3.4 Nonlinear Moment Problem;453
7.2.4;11.4 Modified Moments Procedure;455
7.2.5;11.5 Optimal Vibration Suppression of a Plate as a Mathematical Programming Problem;460
7.2.6;Problems;464
7.2.7;References;465
7.3;Chapter 12: Structural Theory of Vibration Protection Systems;467
7.3.1;12.1 Operator Characteristics of a Dynamic System;468
7.3.1.1;12.1.1 Types of Operator Characteristics;468
7.3.1.2;12.1.2 Transfer Function;472
7.3.1.3;12.1.3 Elementary Blocks;474
7.3.1.4;12.1.4 Combination of Blocks. Bode Diagram;481
7.3.1.5;12.1.5 Block Diagram Transformations;488
7.3.2;12.2 Block Diagrams of Vibration Protection Systems;490
7.3.2.1;12.2.1 Representation of b-k and b-m Systems as Block Diagram;490
7.3.2.2;12.2.2 Vibration Protection Closed Control System;497
7.3.2.3;12.2.3 Dynamic Vibration Absorber;503
7.3.3;12.3 Vibration Protection Systems with Additional Passive Linkages;505
7.3.3.1;12.3.1 Linkage with Negative Stiffness;505
7.3.3.2;12.3.2 Linkage by the Acceleration;506
7.3.4;12.4 Vibration Protection Systems with Additional Active Linkages;507
7.3.4.1;12.4.1 Functional Schemes of Active Vibration Protection Systems;508
7.3.4.2;12.4.2 Vibration Protection on the Basis of Excitation. Invariant System;509
7.3.4.3;12.4.3 Vibration Protection on the Basis of Object State. Effectiveness Criteria;511
7.3.4.4;12.4.4 Block Diagram of Optimal Feedback Vibration Protection;517
7.3.5;References;521
8;Part III: Shock and Transient Vibration;523
8.1;Chapter 13: Active and Parametric Vibration Protection of Transient Vibrations;524
8.1.1;13.1 Laplace Transform;524
8.1.2;13.2 Heaviside Method;530
8.1.3;13.3 Active Suppression of Transient Vibration;540
8.1.3.1;13.3.1 Step Excitation;540
8.1.3.2;13.3.2 Impulse Excitation;544
8.1.4;13.4 Parametric Vibration Suppression;547
8.1.4.1;13.4.1 Recurrent Instantaneous Pulses;547
8.1.4.2;13.4.2 Recurrent Impulses of Finite Duration;549
8.1.5;References;556
8.2;Chapter 14: Shock and Spectral Theory;557
8.2.1;14.1 Concepts of Shock Excitation;557
8.2.1.1;14.1.1 Types of Shock Exposures;557
8.2.1.2;14.1.2 Different Approaches to the Shock Problem;559
8.2.1.3;14.1.3 Fourier Transform;565
8.2.1.4;14.1.4 Time and Frequency Domain Concepts;574
8.2.2;14.2 Forced Shock Excitation of Vibration;575
8.2.2.1;14.2.1 Heaviside Step Excitation;576
8.2.2.2;14.2.2 Step Excitation of Finite Duration;578
8.2.2.3;14.2.3 Impulse Excitation [15, 17, 25];581
8.2.3;14.3 Kinematic Shock Excitation of Vibration;582
8.2.3.1;14.3.1 Forms of the Vibration Equation;583
8.2.3.2;14.3.2 Response of a Linear Oscillator to Acceleration Impulse;584
8.2.4;14.4 Spectral Shock Theory;586
8.2.4.1;14.4.1 Biot´s Dynamic Model of a Structure: Primary and Residual Shock Spectrum;587
8.2.4.2;14.4.2 Response Spectra for the Simplest Vibration Protection System;589
8.2.4.3;14.4.3 Spectral Method for Determination of Response;590
8.2.5;14.5 Brief Comments on the Various Methods of Analysis;592
8.2.6;References;597
8.3;Chapter 15: Statistical Theory of the Vibration Protection Systems;599
8.3.1;15.1 Random Processes and Their Characteristics;600
8.3.1.1;15.1.1 Probability Distribution and Probability Density;601
8.3.1.2;15.1.2 Mathematical Expectation and Dispersion;603
8.3.1.3;15.1.3 Correlational Function;606
8.3.2;15.2 Stationary Random Processes;608
8.3.2.1;15.2.1 Properties of Stationary Random Processes;608
8.3.2.2;15.2.2 Ergodic Processes [12];611
8.3.2.3;15.2.3 Spectral Density;612
8.3.2.4;15.2.4 Transformations of Random Exposures by a Linear System;615
8.3.3;15.3 Dynamic Random Excitation of a Linear Oscillator;620
8.3.3.1;15.3.1 Transient Vibration Caused by Impulse Shock;621
8.3.3.2;15.3.2 Force Random Excitation;625
8.3.4;15.4 Kinematic Random Excitation of Linear Oscillator;629
8.3.4.1;15.4.1 Harmonic and Polyharmonic Excitations;629
8.3.4.2;15.4.2 Shock Vibration Excitation by a Set of Damped Harmonics;635
8.3.5;References;639
9;Part IV: Special Topics;641
9.1;Chapter 16: Rotating and Planar Machinery as a Source of Dynamic Exposures on a Structure;642
9.1.1;16.1 Dynamic Pressure on the Axis of a Rotating Body;642
9.1.2;16.2 Types of Unbalancing Rotor;646
9.1.2.1;16.2.1 Static Unbalance;646
9.1.2.2;16.2.2 Couple Unbalance;647
9.1.2.3;16.2.3 Dynamic Unbalance;647
9.1.2.4;16.2.4 Quasi-Static Unbalance;648
9.1.3;16.3 Shaking Forces of a Slider Crank Mechanism;649
9.1.3.1;16.3.1 Dynamic Reactions;651
9.1.3.2;16.3.2 Elimination of Dynamic Reactions;654
9.1.4;References;659
9.2;Chapter 17: Human Operator Under Vibration and Shock;660
9.2.1;17.1 Introduction;660
9.2.1.1;17.1.1 Vibration Exposures and Methods of Their Transfer on the Person;661
9.2.1.2;17.1.2 International and National Standards;665
9.2.2;17.2 Influence of Vibration Exposure on the Human Subject;665
9.2.2.1;17.2.1 Classification of the Adverse Effects of Vibration on the Person;666
9.2.2.2;17.2.2 Effect of Vibration on the Human Operator;668
9.2.3;17.3 Vibration Dose Value;672
9.2.4;17.4 Mechanical Properties and Frequency Characteristics of the Body;676
9.2.4.1;17.4.1 Mechanical Properties of the Human Body;677
9.2.4.2;17.4.2 Frequency Characteristics of the Human Body;679
9.2.5;17.5 Models of the Human Body;682
9.2.5.1;17.5.1 Basic Dynamic 1D Models;684
9.2.5.2;17.5.2 Dynamic 2D-3D Models of the Sitting Human Body at the Collision;688
9.2.5.3;17.5.3 Parameters of the Human Body Model;690
9.2.6;References;694
10;Appendix A: Complex Numbers;697
10.1;A.1 Complex Conjugate Numbers;697
10.2;A.2 Algebraic Procedures;698
11;Appendix B: Laplace Transform;700
11.1;References;702
12;Index;703