About the Book
Table of Contents:
Preface xi 1 Introduction 1
1.1 Models of Systems, 4
1.2 Systems, Subsystems, and Components, 7
1.3 State-Determined Systems, 9
1.4 Uses of Dynamic Models, 10
1.5 Linear and Nonlinear Systems, 11
1.6 Automated Simulation, 12
References, 13
Problems, 14
2 Multiport Systems and Bond Graphs 17
2.1 Engineering Multiports, 17
2.2 Ports, Bonds, and Power, 24
2.3 Bond Graphs, 27
2.4 Inputs, Outputs, and Signals, 30
Problems, 33
3 Basic Bond Graph Elements 37
3.1 Basic 1-Port Elements, 37
3.2 Basic 2-Port Elements, 50
3.3 The 3-Port Junction Elements, 57
3.4 Causality Considerations for the Basic Elements, 63
3.4.1 Causality for Basic 1-Ports, 64
3.4.2 Causality for Basic 2-Ports, 65
3.4.3 Causality for Basic 3-Ports, 66
3.5 Causality and Block Diagrams, 67
Reference, 71
Problems, 71
4 System Models 77
4.1 Electrical Systems, 78
4.1.1 Electrical Circuits, 78
4.1.2 Electrical Networks, 84
4.2 Mechanical Systems, 91
4.2.1 Mechanics of Translation, 91
4.2.2 Fixed-Axis Rotation, 100
4.2.3 Plane Motion, 106
4.3 Hydraulic and Acoustic Circuits, 121
4.3.1 Fluid Resistance, 122
4.3.2 Fluid Capacitance, 125
4.3.3 Fluid Inertia, 130
4.3.4 Fluid Circuit Construction, 132
4.3.5 An Acoustic Circuit Example, 135
4.4 Transducers and Multi-Energy-Domain Models, 136
4.4.1 Transformer Transducers, 137
4.4.2 Gyrator Transducers, 139
4.4.3 Multi-Energy-Domain Models, 142
References, 144
Problems, 144
5 State-Space Equations and Automated Simulation 162
5.1 Standard Form for System Equations, 165
5.2 Augmenting the Bond Graph, 168
5.3 Basic Formulation and Reduction, 175
5.4 Extended Formulation Methods—Algebraic Loops, 183
5.4.1 Extended Formulation Methods—Derivative Causality, 188
5.5 Output Variable Formulation, 196
5.6 Nonlinear and Automated Simulation, 198
5.6.1 Nonlinear Simulation, 198
5.6.2 Automated Simulation, 202
Reference, 207
Problems, 207
6 Analysis and Control of Linear Systems 218
6.1 Introduction, 218
6.2 Solution Techniques for Ordinary Differential Equations, 219
6.3 Free Response and Eigenvalues, 222
6.3.1 A First-Order Example, 223
6.3.2 Second-Order Systems, 225
6.3.3 Example: The Undamped Oscillator, 230
6.3.4 Example: The Damped Oscillator, 232
6.3.5 The General Case, 236
6.4 Transfer Functions, 239
6.4.1 The General Case for Transfer Functions, 241
6.5 Frequency Response, 244
6.5.1 Example Transfer Functions and Frequency Responses, 249
6.5.2 Block Diagrams, 255
6.6 Introduction to Automatic Control, 258
6.6.1 Basic Control Actions, 259
6.6.2 Root Locus Concept, 273
6.6.3 General Control Considerations, 285
6.7 Summary, 310
References, 311
Problems, 311
7 Multiport Fields and Junction Structures 326
7.1 Energy-Storing Fields, 327
7.1.1 C-Fields, 327
7.1.2 Causal Considerations for C-Fields, 333
7.1.3 I -Fields, 340
7.1.4 Mixed Energy-Storing Fields, 348
7.2 Resistive Fields, 350
7.3 Modulated 2-Port Elements, 354
7.4 Junction Structures, 357
7.5 Multiport Transformers, 359
References, 364
Problems, 365
8 Transducers, Amplifiers, and Instruments 371
8.1 Power Transducers, 372
8.2 Energy-Storing Transducers, 380
8.3 Amplifiers and Instruments, 385
8.4 Bond Graphs and Block Diagrams for Controlled Systems, 392
References, 397
Problems, 397
9 Mechanical Systems with Nonlinear Geometry 411
9.1 Multidimensional Dynamics, 412
9.1.1 Coordinate Transformations, 416
9.2 Kinematic Nonlinearities in Mechanical Dynamics, 420
9.2.1 The Basic Modeling Procedure, 422
9.2.2 Multibody Systems, 433
9.2.3 Lagrangian or Hamiltonian IC -Field Representations, 440
9.3 Application to Vehicle Dynamics, 445
9.4 Summary, 452
References, 452
Problems, 453
10 Distributed-Parameter Systems 470
10.1 Simple Lumping Techniques for Distributed Systems, 471
10.1.1 Longitudinal Motions of a Bar, 471
10.1.2 Transverse Beam Motion, 476
10.2 Lumped Models of Continua through Separation of Variables, 482
10.2.1 The Bar Revisited, 483
10.2.2 Bernoulli–Euler Beam Revisited, 491
10.3 General Considerations of Finite-Mode Bond Graphs, 499
10.3.1 How Many Modes Should Be Retained?, 499
10.3.2 How to Include Damping, 503
10.3.3 Causality Consideration for Modal Bond Graphs, 503
10.4 Assembling Overall System Models, 508
10.5 Summary, 512
References, 512
Problems, 512
11 Magnetic Circuits and Devices 519
11.1 Magnetic Effort and Flow Variables, 519
11.2 Magnetic Energy Storage and Loss, 524
11.3 Magnetic Circuit Elements, 528
11.4 Magnetomechanical Elements, 532
11.5 Device Models, 534
References, 543
Problems, 544
CONTENTS ix
12 Thermofluid Systems 548
12.1 Pseudo-Bond Graphs for Heat Transfer, 548
12.2 Basic Thermodynamics in True Bond Graph Form, 551
12.3 True Bond Graphs for Heat Transfer, 558
12.3.1 A Simple Example of a True Bond Graph Model, 561
12.3.2 An Electrothermal Resistor, 563
12.4 Fluid Dynamic Systems Revisited, 565
12.4.1 One-Dimensional Incompressible Flow, 569
12.4.2 Representation of Compressibility Effects in True Bond Graphs, 573
12.4.3 Inertial and Compressibility Effects in One-Dimensional Flow, 576
12.5 Pseudo-Bond Graphs for Compressible Gas Dynamics, 578
12.5.1 The Thermodynamic Accumulator—A Pseudo-Bond Graph Element, 579
12.5.2 The Thermodynamic Restrictor—A Pseudo-Bond Graph Element, 584
12.5.3 Constructing Models with Accumulators and Restrictors, 587
12.5.4 Summary, 590
References, 592
Problems, 592
13 Nonlinear System Simulation 600
13.1 Explicit First-Order Differential Equations, 601
13.2 Differential Algebraic Equations Caused by Algebraic Loops, 604
13.3 Implicit Equations Caused by Derivative Causality, 608
13.4 Automated Simulation of Dynamic Systems, 612
13.4.1 Sorting of Equations, 613
13.4.2 Implicit and Differential Algebraic Equation Solvers, 614
13.4.3 Icon-Based Automated Simulation, 614
13.5 Example Nonlinear Simulation, 616
13.5.1 Some Simulation Results, 620
13.6 Summary, 623
References, 624
Problems, 624
Appendix: Typical Material Property Values Useful in Modeling
Mechanical, Acoustic, and Hydraulic Elements 630
Index 633
About the Author :
DEAN C. KARNOPP and DONALD L. MARGOLIS are Professors of Mechanical Engineering at the University of California, Davis. RONALD C. ROSENBERG is Professor of Mechanical Engineering at Michigan State University. The authors have extensive experience in teaching system dynamics at the graduate and undergraduate levels and have published numerous papers on the industrial applications of the subject.
