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.

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

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