Engineering system dynamics: a unified graph-centered approach
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
CRC, Taylor & Francis
2007
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Physical Description: | XIX, 1058 S. graph. Darst. |
| ISBN: | 9780849396489 0849396484 1420009583 |
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MARC
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| _version_ | 1804135972448763904 |
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| adam_text | Titel: Engineering system dynamics
Autor: Brown, Forbes T
Jahr: 2007
Contents
Table of Bond Graph Elements inside front cover
Preface xv
To the Instructor xvii
Chapter 1 INTRODUCTION 1
1.1 Example; 1.2 Modeling and Engineering Science; 1.3 Modeling Languages;
1.4 Modeling for Control; 1.5 A Word to the Wise About Learning; 1.6 Treat¬
ment of Dimensions; 1.7 Treatment of Units; References
Chapter 2 SOURCE-LOAD SYNTHESIS 15
2.1 System Reticulation 15
2.1.1 Case Study: Induction Motor as a Source; 2.1.2 Case Study: Water Sprin¬
kler System as a Load; 2.1.3 The Source-Load Synthesis: Case Study; 2.1.4
Summary
2.2 Generalized Forces and Velocities 25
2.2.1 Efforts and Flows; 2.2.2 Electric Conductors; 2.2.3 Longitudinal Mechan¬
ical Motion; 2.2.4 Incompressible Fluid Flow; 2.2.5 Rotational Motion; 2.2.6
Lateral Mechanical Motion; 2.2.7 Microbonds; 2.2.8 Analogies; 2.2.9 Summary
2.3 Generalized Sources, Sinks and Resistances 34
2.3.1 Independent-Effort and Independent-Flow Sources and Sinks; 2.3.2 General
Sources and Sinks; 2.3.3 Linear Resistances; 2.3.4 Nonlinear Resistances; 2.3.5
Source-Load Synthesis; 2.3.6 Power Considerations; 2.3.7 Summary
2.4 Ideal Machines: Transformers and Gyrators 48
2.4.1 Ideal Machines; 2.4.2 Transformers; 2.4.3 Gyrators; 2.4.4 Mechanical De¬
vices Modeled as Transformers; 2.4.5 Electrical Transformers; 2.4.6 Transducers
Modeled as Transformers; 2.4.7 Mechanical Devices Modeled as Gyrators; 2.4.8
Transducers Modeled as Gyrators; 2.4.9 Summary
2.5 Systems with Transformers and Gyrators 60
2.5.1 Cascaded Transformers; 2.5.2 Cascaded Gyrators; 2.5.3 Case Study of
a Transformer Connecting a Source to a Load; 2.5.4 Second Case Study of a
Transformer Connecting a Source to a Load; 2.5.5 Case Study of a Gyrator
Connecting a Source to a Load; 2.5.6 Transmission Matrices*; 2.5.7 Summary
viii
Chapter 3 SIMPLE DYNAMIC MODELS
77
3.1 Compliance Energy Storage
3.1.1 Linear Springs and Energy; 3.1.2 The Generalized Linear Compliance;
3.1.3 Electric Circuit Compliance; 3.1.4 Linear Fluid Compliance Due to Grav-
ity- 3.1.5 Fluid Compliance Due to Compressibility; 3.1.6 Summary
, 85
3.2 Inertaiice Energy Storage
3.2.1 Mass, Momentum and Kinetic Energy; 3.2.2 The Generalized Linear Iner¬
taiice; 3.2.3 Common Engineering Elements Modeled by Constant Inertanccs;
3.2.4 Tetrahedron of State*; 3.2.5 Summary
92
3.3 Junctions
3.3.1 Junction Types; 3.3.2 Mechanical Constraints Modeled by 1-Junctions;
3.3.3 Electric Circuit Constraints Modeled by 1-Junctions; 3.3.4 Fluid Circuit
Constraints Modeled by 1-Junctions; 3.3.5 Mechanical Constraints Modeled
by 0-J unctions; 3.3.6 Electric and Fluid Circuit Constraints Modeled by 0-
Junctions; 3.3.7 Simple IRC Models; 3.3.8 Summary
3.4 Causality and Differential Equations 112
3.4.1 Operational Block Diagrams; 3.4.2 Causal Bond Graphs; 3.4.3 Junctions
with Elements Having Uncoupled Behavior; 3.4.4 Junctions with Elements Hav¬
ing Coupled Behavior; 3.4.5 Writing Differential Equations; 3.4.6 Summary
3.5 Nonlinear Resistances, Compliances and Inertances 127
3.5.1 Nonlinear Resistances; 3.5.2 Nonlinear Compliances; 3.5.3 Nonlinear Fluid
Compliance Due to Gravity; 3.5.4 Nonlinear Compressibility Compliance; 3.5.5
Junctions with Multiple Bonded Compliances; 3.5.6 Nonlinear Inertances; 3.5.7
Kinetic and Potential Energies and Co-Energies; 3.5.8 Summary
3.6 Numerical Simulation 138
3.6.1 State-Variable Differential Equations; 3.6.2 Simulation With ODE Rou¬
tines of MATLAB; 3.6.3 Simulation With Simulink*; 3.6.4 Integration Algo¬
rithms; 3.G.5 Second-Order Runge-Kutta; 3.6.6 Fourth-Order Runge-Kutta;
3.6.7 Summary
Chapter 4 ANALYSIS OF LINEAR MODELS, PART 1 155
4.1 Linear Models and Simulation 155
4.1.1 Superposition and Linearity; 4.1.2 Linearity and Differential Equations;
4.1.3 Operator Notation; 4.1.4 Transformation from State-Space to Scalar Form;
4.1.5 Transformation from Scalar to State-Space Form*; 4.1.6 Transformations
Using MATLAB©; 4.1.7 Simulation of Linear Models Using MATLAB*; 4.1.8
Simulation of Linear Models Using Simulink*; 4.1.9 Summary
4.2 Common Functions in Excitations and Responses 169
4.2.1 Exponential Functions; 4.2.2 Singularity Functions; 4.2.3 Summary
4.3 Direct Solutions of Linear Differential Equations 174
4 3 ! T!U; °Am°fneOUS S°1Uti0n; 4 3 2 The Method of Undetermined Coeffi-
4 V n ff AfPPf atl011°If Initial Conditi »s; 4.3.4 Solutions to Impulse Inputs;
4.3.o Differentiation and Integration Properties; 4.3.6 Summary
IX
4.4 Convolution* 186
4.4.1 Decomposing Signals into a Sum of Steps; 4.4.2 Discrete Convolution; 4.4.3
Discrete Convolution by MATLAB; 4.4.4 Convolution Integrals; 4.4.5 Summary
4.5 The Laplace Transform 197
4.5.1 Definition and Inverse; 4.5.2 The Derivative Relations; 4.5.3 Singularity
Functions and Discontinuities; 4.5.4 Other Key Relations; 4.5.5 Finding Laplace
Transforms of Output Variables; 4.5.6 Finding Inverse Transforms: Partial
Fraction Expansions; 4.5.7 Initial and Final Value Theorems; 4.5.8 Develop¬
ment of the Laplace Transform from the Fourier Transform*; 4.5.9 Development
of the Laplace Transform from the Convolution Integral*; 4.5.10 Summary
4.6 Responses of Primitive Linear Models 217
4.6.1 Responses of First-Order Models; 4.6.2 Responses of Second-Order Models
to Initial Conditions; 4.6.3 Responses of Second-Order Models to Step and
Impulse Excitations; 4.6.4 Step and Impulse Responses Using MATLAB; 4.6.5
Summary
4.7 Linearization 233
4.7.1 Case Study with Linearization of a Resistance; 4.7.2 Linearization of a
Function of One Variable; 4.7.3 Essential Nonlinearities; 4.7.4 Linearization of
a Function of Two Variables; 4.7.5 Linearization of a First-Order Differential
Equation; 4.7.6 Linearization of State-Variable Differential Equations; 4.7.7
Case Study with Three Different Types of Equilibria; 4.7.8 Summary
Chapter 5 BASIC MODELING 257
5.1 Simple Circuits 257
5.1.1 Simple Electric Circuits; 5.1.2 Fluid Circuits; 5.1.3 Mechanical Circuits;
5.1.4 Use of Energy Integrals; 5.1.5 Summary
5.2 System Models with Ideal Machines 272
5.2.1 Electric Circuits; 5.2.2 Fluid/Mechanical Circuits; 5.2.3 Losses in Positive
Displacement Machines*; 5.2.4 Losses With DC Motor/Generators*; 5.2.5 Case
Study with Source and Load*; 5.2.6 Two- and Three-Diinensional Geometric
Constraints; 5.2.7 Case Study: Pulley System; 5.2.8 Model Structure from
Energy Expressions; 5.2.9 Modeling Guidelines; 5.2.10 Tutorial Case Study;
5.2.11 Common Misconceptions; 5.2.12 Summary
5.3 Model Equivalences 307
5.3.1 Thevenin and Norton Equivalent Sources and Loads; 5.3.2 Passivity With
Respect to a Point on a Characteristic*; 5.3.3 Truncation of Transformers and
Gyrators Bonded to R, C or I Elements; 5.3.4 Reduction of Two-Pair Meshes;
5.3.5 Transmission Matrix Reduction of Steady-State Models*; 5.3.6 Summary
5.4 Equilibrium 323
5.4.1 Reduction of Steady-State Models with a Single Source: Case Study; 5.4.2
Alternative Approaches to Reducing Steady-State Models; 5.4.3 Removal of
Elements for Equilibrium; 5.4.4 Case Study with a Steady-Velocity Equilibrium;
5.4.5 Case Study with Stable and Unstable Static Equilibria; 5.4.6 Case Study
with Limit-Cycle Behavior; 5.4.7 Necessary Condition for Instability or Limit-
Cycle Oscillation*; 5.4.8 Summary
X
Chapter C MATHEMATICAL FORMULATION FROM BOND GRAPHS.343
. , „ 343
C.l Causality and Differential Equations
G 1 1 Applying Causal Strokes; 6.1.2 Differential Equations for Causal Models;
(i.1.3 Case Study: A Linear Circuit; 6.1.4 Case Study: Nonlinear Stick-Slip,
6.1.5 Case Study with Transformers and Gyrators; 6.1.6 Models Reducible to
Causal Form; Order of a Model; 6.1.7 Summary ¦
G.2 Over-Causal and Under-Causal Models 370
6.2.1 Treatment of Over-Causal Models; Case Study; 6.2.2 Equations for Under-
Causal Models; 6.2.3 Algebraic Reduction Method; Case Study; 6.2.4 Differenti¬
ation Method; Case Study*; 6.2.5 Method of Non-Zero Virtual Energy-Storages;
Case Study Continued; 6.2.6 Commercial Software for DAEs; 6.2.7 Case Study
with Meshes; 6.2.8 Summary
G.3 The Loop Rule* 401
6.3.1 Signal Flow Graphs; 6.3.2 The Loop Rule for Signal Flow Graphs; 6.3.3
Converting Bond Graphs to Signal Flow Graphs; 6.3.4 Direct Application of the
Loop Rule to Bond Graphs Without Meshes; 6.3.5 Bond Graphs with Meshes;
6.3.6 Determination of State Differential Equations; 6.3.7 Summary
Chapter 7 ANALYSIS OF LINEAR MODELS, PART 2 419
7.1 Sinusoidal Frequency Response 419
7.1.1 The Phasor Method; 7.1.2 Bode Plots; 7.1.3 Models Comprising a Sin¬
gle Pole or Zero; 7.1.4 Models Comprising a Pair of Complex Poles or Zeros;
7.1.5 Factorization of Higher-Order Models; 7.1.6 Bode Plots for Higher-Order
Models*; 7.1.7 The Pure Delay Operator*; 7.1.8 Summary
7.2 Mechanical Vibrations 456
7.2.1 Case Study: Rotating Unbalanced Mass; 7.2.2 Case Study: Tuned Vi¬
bration Absorber; 7.2.3 Modes of Motion; 7.2.4 Case Study: Untuned Viscous
Damper; 7.2.5 Summary
7.3 Matrix Representation of Dynamic Behavior* 471
7..1.1 llie Matrix Exponential; 7.3.2 Response to a Linearly Varying Excita¬
tion; 7.3.3 Eigenvalues, Eigenvectors and Modes; 7.3.4 Case Study: Three Fluid
Tanks; 7.3.5 Case Study with Complex Roots; 7.3.6 Modified Method for Com¬
plex Eigenvalues*; 7.3.7 Case Study: Vehicle Dynamics; 7.3.8 Application of
MATLAB; 7.3.9 Response to Exponential and Frequency Excitations; 7.3.10
Representation in the s-Plane; 7.3.11 Summary
7.4 Fourier Analysis
7.4.1 Fourier Series; 7.4.2 Response of a Linear System to a Periodic Excitation;
n mat! FnTf!T; 7AA Digital SPectral Analysis*; 7.4.5 Fourier Analysis
Using MATLAB ; 7.4.6 Summary
Chapter 8 INTRODUCTION TO AUTOMATIC CONTROL 519
8.1 Open- and Closed-Loop Control 51g
Summary
XI
8.2 Dynamic Compensation 539
8.2.1 Proportional-Plus-Integral Control; 8.2.2 Proportional-Plus-Derivative
Control; 8.2.3 Proportional-Plus-Integral-Plus-Derivative Control; 8.2.4 Phase
Lead Controllers; 8.2.5 Phase Lag Controllers; 8.2.6 Phase Lead-Lag Con¬
trollers; 8.2.7 Digital Control Systems; 8.2.8 Summary
8.3 Frequency Response Methods 558
8.3.1 Polar or Nyquist Frequency Response Plots; 8.3.2 The Nyquist Stabil¬
ity Criterion; 8.3.3 Measures of Relative Stability; 8.3.4 Nichols Charts; 8.3.5
Dynamic Compensation Using Nichols Charts; 8.3.6 Approximate Correction
for Digital Sampling; 8.3.7 Special Roles for Bond Graphs in Control System
Design; 8.3.8 Summary
Chapter 9 EXTENDED MODELING 583
9.1 Modulated Transformers 583
9.1.1 Remotely Modulated Transformers; 9.1.2 Locally Modulated Transform¬
ers; 9.1.3 Increase in the Order of a Model Due to Modulation; 9.1.4 Dependent
Inertance with a Locally Modulated Transformer; 9.1.5 Inertancc Dependent
on Local Displacement; Case Study; 9.1.6 Summary
9.2 Activated Bonds 604
9.2.1 Definition and Application; 9.2.2 Causality; 9.2.3 Summary
9.3 Linear Multiport Fields 616
9.3.1 Linear Two-Port Inertance: The Electric Transformer; 9.3.2 Linear Two-
port Inertance: The Rigid Inertive Floating Link; 9.3.3 Linear Two-Port Com¬
pliance: The Piezoelectric Transducer; 9.3.4 Linear Two-Port Compliance: The
Piezomagnetic (Magnetostrictive) Transducer; 9.3.5 Linear Two-Port Compli¬
ance: The Thermoelastic Rod; 9.3.6 Linear Multiport Compliances: Gener¬
alized Linear Media*; 9.3.7 Reticulation of General Linear Multiport Fields*;
9.3.8 Summary
9.4 Nonlinear Multiport Fields 633
9.4.1 Nonlinear Compliance Fields: Generic Relationships; 9.4.2 Examples with
Geometrically Varied Capacitance; 9.4.3 Nonlinear Multiport Incrtances; 9.4.4
Inertances Dependent on Holonomic Constraints; 9.4.5 Inertances Dependent
on Nonholonomic Constraints; 9.4.6 Summary
9.5 Magnetic Circuits 651
9.5.1 Magnetic Effort, Flow and Compliance; 9.5.2 Generation of Mechanical
Forces; 9.5.3 First-Order Treatment of Permanent Magnets: A Case Study;
9.5.4 Flux Fringing and Leakage; 9.5.5 Eddy-Current Losses; 9.5.6 Saturation
and Hysteresis; 9.5.7 Simulation with Hysteresis*; 9.5.8 RC Element with Me¬
chanical Port*; 9.5.9 Summary
9.6 Electric Motors 681
9.6.1 Vector Bonds and Transformers; 9.6.2 Synchronous Motor/Brushless D.C.
Motor; 9.6.3 Three-Phase Induction Motors; 9.6.4 Single-Phase Induction Mo¬
tors; 9.6.5 Stepping Motors; 9.6.6 Summary
xii
694
9.7 Irreversible Couplers and Thermal Systems • • • ¦
9.7.1 Kffort and Flow Variables; 9.7.2 Heat Conduction; 9.7.3 The Irreversibility
Coupler; 9.7.4 Application to Friction; 9.7.5 Use of 0- and 1- Junctions, 9.7.6
Thermal Compliance; 9.7.7 Pseudo Bond Graphs for Heat Conduction, 9.7.8
Thermodynamic Coupling Between Mechanical and Thermal Energies, 9.7.9
Lead-Acid Battery: Use of Legendrc Transformation; 9.7.10 Summary
DISTRIBUTED-PARAMETER MODELS 711
Chapter 10
10
10.1.1 Camparison of Lumped and Distributed Models; 10.1.2 The Pure
.lWave Models with Simple Boundary Conditions 712
Bilateral-Wave-Delay Model; 10.1.3 Analysis of the Pure Bilateral-Wave-Delay
Model; 10.1.1 Fixed and Free Boundary Conditions; 10.1.5 Fourier Analysis
with Fixed or Free Boundary Conditions*; 10.1 6 The Hodograph Plane; 10.1.7
Summary
10.2 One-Dimensional Models 72^
10,2.1 General Formulation; 10.2.2 One-Power Models; 10.2.3 Symmetric One-
Power Models; 10.2.4 Multiple-Power Models; 10.2.5 Summary
10.3 Wave Propagation 35
10.3.1 Simplest Model: Pure Transport; 10.3.2 First Modification: Thermal
Leakage to a Constant-Temperature Environment; 10.3.3 Second Modification:
Thermal Compliance in the Walls; 10.3.4 Dispersion and Absorption; 10.3.5
Group Velocity*; 10.3.6 Summary
10.4 One-Power Symmetric Models 745
10,1.1 Wave Behavior; 10.4.2 Energy Velocity in Conservative Media*; 10.4.3
Boundary-Value Problems; Transmission Matrices; 10.4.4 Exponentially Ta¬
pered Systems*; 10.4.5 Summary
10.5 Multiple-Power Models 763
10.5.1 Symmetric and Anti-Symmetric Variables and Models; 10.5.2 Case Study
of a Degenerate System: A Counterflow Heat Exchanger; 10.5.3 Case Study of
a Symmetric Model: The Bernoulli-Euler Beam; 10.5.4 Summary
10.0 Models of Dissipative Processes 709
10.6.1 The Uniform Constant IRC Model; 10.6.2 Fluid Line Dynamics; 10.6.3
The Skin Effect in Electrical Conductors; 10.6.4 The Maxwell Model; 10.6.5
I lie Voigt. Model; 10.G.G The Linear Elastic Solid; 10.6.7 Simulation of Coupled
Storage and Dissipation Fields; 10.6.8 Example of Viscous Effects in Laminar
Flow in a Tube; 10.6.9 Example of Heat Transfer Effects in a Cylindrical Ac¬
cumulator; 10.6.10 Summary
10.7 Wave-Scattering Variables
!n7-«T,hBMr7n^i0n; 10 7 2 SinSlo-Powcr Uniform Symmetric Models;
- - he Method of Characteristics for Pure Bilateral Waves; 10 7 4 General-
rw; N ,1-Syl m ;tiy Cases; 10.7.5 The Quasi Method of Characteristics;
Tlu- Bernoulli-Euler Beam; 10.7.7 Summary
10.8 Internal Excitation*
rs ™ sok, ° - a,m:,
xl *— - » ««
10.9 Modal Decomposition
815
10.9.1 General Procedure; 10.9.2 Sinusoidal Modes: Example of a Plucked
String; 10.9.3 Sinusoidal Modes: Example of a Struck Simply-Supported Beam;
10.9.4 Bond-Graph Modeling; 10.9.5 Modes with Effort-Free Boundaries: Ex¬
ample of a Bernoulli-Euler Beam; 10.9.6 Avoiding Differential Causality; 10.9.7
Summary
10.10 Complex Compound Systems: A Case Study* 832
10.10.1 A Model for Uniform Straight Tubing; 10.10.2 A Model for Uniformly
Curved Tubing; 10.10.3 The Rotation Matrix; 10.10.4 The Transmission Matrix
for a Cascade of Tubes; 10.10.5 Three-Port Junctions; 10.10.6 Added Lumped
Impedances; 10.10.7 Boundary Conditions; 10.10.8 Power Flow and Energy
Density; 10.10.9 Computational and Experimental Example; 10.10.10 Summary
Chapter 11 THERMODYNAMIC SYSTEMS 851
11.1 The Convection Bond and Compressible Flow 851
11.1.1 Flow Through a Port; 11.1.2 The Convection Bond; 11.1.3 The 125 Ele¬
ment for Fluid Flow; 11.1.4 Summary
11.2 Heat Interaction and Junctions 858
11.2.1 The Reversible Heat Interaction Element; 11.2.2 The General Heat In¬
teraction Element; 11.2.3 The HRS Macro Element; 11.2.4 The 0-Junction for
Convection Bonds; 11.2.5 Merging Streams: The OS Junction; 11.2.6 The 1-
Junction and lS-Junction with Convection; 11.2.7 Summary
11.3 Case Study with Quasi-Steady Flow* 871
11.3.1 The Bond Graph Model; 11.3.2 Irreversibilities; 11.3.3 Computation of
Results
11.4 Thermodynamic Compliance and Inertance 876
11.4.1 Application of a Simple Thermal Compliance; 11.4.2 Causality; 11.4.3
General Thermodynamic Compliance; 11.4.4 The CS Macro Element; 11.4.5
Computations for the Ideal Gas; 11.4.6 Case Study: A Piston-Cylinder Com¬
pressor; 11.4.7 Treatment of a Quasi-Steady-State Fluid Machine; 11.4.8 Pseudo
Bond Graphs for Compressible Thermofluid Systems; 11.4.9 Fluid Inertance and
Area Change With Compressible Flow; 11.4.10 Summary
11.5 Evaluation of Thermodynamic Properties 897
11.5.1 The Most Commonly Available Analytical Form for State Properties;
11.5.2 Helmholtz Analytical Form for State Properties; 11.5.3 Application to
Gases; 11.5.4 Application to Refrigerants; 11.5.5 Application to Water; 11.5.6
Saturated Vapor Density for Other Substances; 11.5.7 Case Study: A Refriger¬
ation Cycle; 11.5.8 Application to the Liquid Region; 11.5.9 Considerations of
Reversing Flows; 11.5.10 Simulation with Fluid Kinetic Energy; 11.5.11 Heat
Transfer Equations for Three-Phase CS1 Elements; 11.5.12 Summary
11.6 Systems with Chemical Reaction* 929
11.6.1 Energy of a Pure Substance; 11.6.2 Energy of Multiple Species; 11.6.3
Stoichoimetric Coefficients and Reaction Forces; 11.6.4 Chemical Equilibrium;
11.6.5 Reaction Rates; 11.6.6 Models of Reactions without Mass Flows; 11.6.7
Models of Reactions with Mass Flows; 11.6.8 Summary
xiv
Chapter 12 TOPICS IN ADVANCED MODELING 937
937
12.1 Field Lumping.
.1.1 Scalar Fields; 12.1.2 Rigid-Body Vector Fields; 12.1.3 The Role of App¬
roximations; 12.1.4 Nodic Fields; 12.1.5 Planar Vector Nodic Fields; 12.1.6
Estimating Upper and Lower Bounds for Field Transnuttances ; 12.1.7 Three-
Dimensional Vector Nodic Fields; 12.1.8 Near-Spherical Fields; 12.1.9 Near-
Cvlindrical Fields; 12.1.10 Multiport Vector Nodic Fields; 12.1.11 Summary
955
12.2 Nonconservative Couplers
12.2.1 Causal Relations; 12.2.2 Equilibrium; 12.2.3 Dimensional Analysis; 12.2.4
Dynamic Simulation; 12.2.5 Linear Couplers; 12.2.6 Summary
12.3 Lagrange s Equations for Holonomic Systems 972
12.3.1 Primitive Coordinates and Velocities; 12.3.2 Holonomic Constraints;
12.3.3 Lagrange s Equations; 12.3.4 Example of a Solenoid; 12.3.5 Summary
12.4 Lagrangian Bond Graphs; Dissipation 981
12.4.1 Shorthand Notation; 12.4.2 Detailed Lagrangian Bond Graphs; 12.4.3
Example of the Flyball Governor; 12.4.4 Example of a Vibratory Rate Gyro;
12.4.5 Dissipation; 12.4.G Summary
12.5 Nonholonomic Constraints 988
12.5.1 Case Study: Variable-Flywheel Energy Storage for Vehicles; 12.5.2
Analysis and Representation of Nonholonomic Systems; 12.5.3 Application to
Case Study; 12.5.4 Example of the Rolling Penny; 12.5.5 Irreversible Nonholo¬
nomic Constraints; 12.5.6 The Umbra-Lagrangian of Mukherjee; 12.5.7 Sum¬
mary
12.6 Hamilton s Equations and Bond Graphs* 1000
12.6.1 Hamilton s Equations; 12.6.2 Hamiltonian Bond Graphs; 12.6.3 Applica¬
tion to Flyball Governor; 12.6.4 Example of a Seating Valve Using Lagrange s
Equations; 12.6.5 Hamilton s Equations for the Seating Valve; 12.6.6 Viscous
Dissipation; 12.6.7 Summary
APPENDIX A INTRODUCTION TO MATLAB® 1009
Scalar Calculations; Variables; Complex Numbers; Arrays and Matrices; Evalu¬
ating and Plotting Functions; Fitting Curves to Data; Control Flow Commands;
Script Files; Data Files; Function Files; Communication Between Files; MAT-
LAB Files Downloadable from the Internet
APPENDIX B CLASSICAL VIBRATIONS 1021
B.l Models with Two Degrees of Freedom 1021
B.l.l Normal Mode Vibration; B.l.2 Forced Harmonic Motion
B.2 Higher-Order Models ^3
n n l M0,!a! °tioilS; B-2 2 Tho Initial Value Problem; B.2.3 Forced Response;
11.2.4 Modal Damping; B.2.5 Example Using MATLAB; B.2.6 Mode Reduction
APPENDIX C LAPLACE TRANSFORM PAIRS 1033
APPENDIX D THERMODYNAMIC DATA AND COMPUTER CODE. . 1037
D.l Programs and Data for Air and Components; D.2 Programs and Data for
Data for wLcr D 3 ^ Refrigerant R22! D4 Programs and
Index
|
| adam_txt |
Titel: Engineering system dynamics
Autor: Brown, Forbes T
Jahr: 2007
Contents
Table of Bond Graph Elements inside front cover
Preface xv
To the Instructor xvii
Chapter 1 INTRODUCTION 1
1.1 Example; 1.2 Modeling and Engineering Science; 1.3 Modeling Languages;
1.4 Modeling for Control; 1.5 A Word to the Wise About Learning; 1.6 Treat¬
ment of Dimensions; 1.7 Treatment of Units; References
Chapter 2 SOURCE-LOAD SYNTHESIS 15
2.1 System Reticulation 15
2.1.1 Case Study: Induction Motor as a Source; 2.1.2 Case Study: Water Sprin¬
kler System as a Load; 2.1.3 The Source-Load Synthesis: Case Study; 2.1.4
Summary
2.2 Generalized Forces and Velocities 25
2.2.1 Efforts and Flows; 2.2.2 Electric Conductors; 2.2.3 Longitudinal Mechan¬
ical Motion; 2.2.4 Incompressible Fluid Flow; 2.2.5 Rotational Motion; 2.2.6
Lateral Mechanical Motion; 2.2.7 Microbonds; 2.2.8 Analogies; 2.2.9 Summary
2.3 Generalized Sources, Sinks and Resistances 34
2.3.1 Independent-Effort and Independent-Flow Sources and Sinks; 2.3.2 General
Sources and Sinks; 2.3.3 Linear Resistances; 2.3.4 Nonlinear Resistances; 2.3.5
Source-Load Synthesis; 2.3.6 Power Considerations; 2.3.7 Summary
2.4 Ideal Machines: Transformers and Gyrators 48
2.4.1 Ideal Machines; 2.4.2 Transformers; 2.4.3 Gyrators; 2.4.4 Mechanical De¬
vices Modeled as Transformers; 2.4.5 Electrical Transformers; 2.4.6 Transducers
Modeled as Transformers; 2.4.7 Mechanical Devices Modeled as Gyrators; 2.4.8
Transducers Modeled as Gyrators; 2.4.9 Summary
2.5 Systems with Transformers and Gyrators 60
2.5.1 Cascaded Transformers; 2.5.2 Cascaded Gyrators; 2.5.3 Case Study of
a Transformer Connecting a Source to a Load; 2.5.4 Second Case Study of a
Transformer Connecting a Source to a Load; 2.5.5 Case Study of a Gyrator
Connecting a Source to a Load; 2.5.6 Transmission Matrices*; 2.5.7 Summary
viii
Chapter 3 SIMPLE DYNAMIC MODELS
77
3.1 Compliance Energy Storage
3.1.1 Linear Springs and Energy; 3.1.2 The Generalized Linear Compliance;
3.1.3 Electric Circuit Compliance; 3.1.4 Linear Fluid Compliance Due to Grav-
ity- 3.1.5 Fluid Compliance Due to Compressibility; 3.1.6 Summary
, 85
3.2 Inertaiice Energy Storage
3.2.1 Mass, Momentum and Kinetic Energy; 3.2.2 The Generalized Linear Iner¬
taiice; 3.2.3 Common Engineering Elements Modeled by Constant Inertanccs;
3.2.4 Tetrahedron of State*; 3.2.5 Summary
92
3.3 Junctions
3.3.1 Junction Types; 3.3.2 Mechanical Constraints Modeled by 1-Junctions;
3.3.3 Electric Circuit Constraints Modeled by 1-Junctions; 3.3.4 Fluid Circuit
Constraints Modeled by 1-Junctions; 3.3.5 Mechanical Constraints Modeled
by 0-J unctions; 3.3.6 Electric and Fluid Circuit Constraints Modeled by 0-
Junctions; 3.3.7 Simple IRC Models; 3.3.8 Summary
3.4 Causality and Differential Equations 112
3.4.1 Operational Block Diagrams; 3.4.2 Causal Bond Graphs; 3.4.3 Junctions
with Elements Having Uncoupled Behavior; 3.4.4 Junctions with Elements Hav¬
ing Coupled Behavior; 3.4.5 Writing Differential Equations; 3.4.6 Summary
3.5 Nonlinear Resistances, Compliances and Inertances 127
3.5.1 Nonlinear Resistances; 3.5.2 Nonlinear Compliances; 3.5.3 Nonlinear Fluid
Compliance Due to Gravity; 3.5.4 Nonlinear Compressibility Compliance; 3.5.5
Junctions with Multiple Bonded Compliances; 3.5.6 Nonlinear Inertances; 3.5.7
Kinetic and Potential Energies and Co-Energies; 3.5.8 Summary
3.6 Numerical Simulation 138
3.6.1 State-Variable Differential Equations; 3.6.2 Simulation With ODE Rou¬
tines of MATLAB; 3.6.3 Simulation With Simulink*; 3.6.4 Integration Algo¬
rithms; 3.G.5 Second-Order Runge-Kutta; 3.6.6 Fourth-Order Runge-Kutta;
3.6.7 Summary
Chapter 4 ANALYSIS OF LINEAR MODELS, PART 1 155
4.1 Linear Models and Simulation 155
4.1.1 Superposition and Linearity; 4.1.2 Linearity and Differential Equations;
4.1.3 Operator Notation; 4.1.4 Transformation from State-Space to Scalar Form;
4.1.5 Transformation from Scalar to State-Space Form*; 4.1.6 Transformations
Using MATLAB©; 4.1.7 Simulation of Linear Models Using MATLAB*; 4.1.8
Simulation of Linear Models Using Simulink*; 4.1.9 Summary
4.2 Common Functions in Excitations and Responses 169
4.2.1 Exponential Functions; 4.2.2 Singularity Functions; 4.2.3 Summary
4.3 Direct Solutions of Linear Differential Equations 174
4'3'! T!U; "°Am°fneOUS S°1Uti0n; 4'3'2 The Method of Undetermined Coeffi-
4 V n ff AfPPf atl011°If Initial Conditi »s; 4.3.4 Solutions to Impulse Inputs;
4.3.o Differentiation and Integration Properties; 4.3.6 Summary
IX
4.4 Convolution* 186
4.4.1 Decomposing Signals into a Sum of Steps; 4.4.2 Discrete Convolution; 4.4.3
Discrete Convolution by MATLAB; 4.4.4 Convolution Integrals; 4.4.5 Summary
4.5 The Laplace Transform 197
4.5.1 Definition and Inverse; 4.5.2 The Derivative Relations; 4.5.3 Singularity
Functions and Discontinuities; 4.5.4 Other Key Relations; 4.5.5 Finding Laplace
Transforms of Output Variables; 4.5.6 Finding Inverse Transforms: Partial
Fraction Expansions; 4.5.7 Initial and Final Value Theorems; 4.5.8 Develop¬
ment of the Laplace Transform from the Fourier Transform*; 4.5.9 Development
of the Laplace Transform from the Convolution Integral*; 4.5.10 Summary
4.6 Responses of Primitive Linear Models 217
4.6.1 Responses of First-Order Models; 4.6.2 Responses of Second-Order Models
to Initial Conditions; 4.6.3 Responses of Second-Order Models to Step and
Impulse Excitations; 4.6.4 Step and Impulse Responses Using MATLAB; 4.6.5
Summary
4.7 Linearization 233
4.7.1 Case Study with Linearization of a Resistance; 4.7.2 Linearization of a
Function of One Variable; 4.7.3 Essential Nonlinearities; 4.7.4 Linearization of
a Function of Two Variables; 4.7.5 Linearization of a First-Order Differential
Equation; 4.7.6 Linearization of State-Variable Differential Equations; 4.7.7
Case Study with Three Different Types of Equilibria; 4.7.8 Summary
Chapter 5 BASIC MODELING 257
5.1 Simple Circuits 257
5.1.1 Simple Electric Circuits; 5.1.2 Fluid Circuits; 5.1.3 Mechanical Circuits;
5.1.4 Use of Energy Integrals; 5.1.5 Summary
5.2 System Models with Ideal Machines 272
5.2.1 Electric Circuits; 5.2.2 Fluid/Mechanical Circuits; 5.2.3 Losses in Positive
Displacement Machines*; 5.2.4 Losses With DC Motor/Generators*; 5.2.5 Case
Study with Source and Load*; 5.2.6 Two- and Three-Diinensional Geometric
Constraints; 5.2.7 Case Study: Pulley System; 5.2.8 Model Structure from
Energy Expressions; 5.2.9 Modeling Guidelines; 5.2.10 Tutorial Case Study;
5.2.11 Common Misconceptions; 5.2.12 Summary
5.3 Model Equivalences 307
5.3.1 Thevenin and Norton Equivalent Sources and Loads; 5.3.2 Passivity With
Respect to a Point on a Characteristic*; 5.3.3 Truncation of Transformers and
Gyrators Bonded to R, C or I Elements; 5.3.4 Reduction of Two-Pair Meshes;
5.3.5 Transmission Matrix Reduction of Steady-State Models*; 5.3.6 Summary
5.4 Equilibrium 323
5.4.1 Reduction of Steady-State Models with a Single Source: Case Study; 5.4.2
Alternative Approaches to Reducing Steady-State Models; 5.4.3 Removal of
Elements for Equilibrium; 5.4.4 Case Study with a Steady-Velocity Equilibrium;
5.4.5 Case Study with Stable and Unstable Static Equilibria; 5.4.6 Case Study
with Limit-Cycle Behavior; 5.4.7 Necessary Condition for Instability or Limit-
Cycle Oscillation*; 5.4.8 Summary
X
Chapter C MATHEMATICAL FORMULATION FROM BOND GRAPHS.343
. , „ 343
C.l Causality and Differential Equations
G 1 1 Applying Causal Strokes; 6.1.2 Differential Equations for Causal Models;
(i.1.3 Case Study: A Linear Circuit; 6.1.4 Case Study: Nonlinear Stick-Slip,
6.1.5 Case Study with Transformers and Gyrators; 6.1.6 Models Reducible to
Causal Form; Order of a Model; 6.1.7 Summary ¦
G.2 Over-Causal and Under-Causal Models 370
6.2.1 Treatment of Over-Causal Models; Case Study; 6.2.2 Equations for Under-
Causal Models; 6.2.3 Algebraic Reduction Method; Case Study; 6.2.4 Differenti¬
ation Method; Case Study*; 6.2.5 Method of Non-Zero Virtual Energy-Storages;
Case Study Continued; 6.2.6 Commercial Software for DAEs; 6.2.7 Case Study
with Meshes; 6.2.8 Summary
G.3 The Loop Rule* 401
6.3.1 Signal Flow Graphs; 6.3.2 The Loop Rule for Signal Flow Graphs; 6.3.3
Converting Bond Graphs to Signal Flow Graphs; 6.3.4 Direct Application of the
Loop Rule to Bond Graphs Without Meshes; 6.3.5 Bond Graphs with Meshes;
6.3.6 Determination of State Differential Equations; 6.3.7 Summary
Chapter 7 ANALYSIS OF LINEAR MODELS, PART 2 419
7.1 Sinusoidal Frequency Response 419
7.1.1 The Phasor Method; 7.1.2 Bode Plots; 7.1.3 Models Comprising a Sin¬
gle Pole or Zero; 7.1.4 Models Comprising a Pair of Complex Poles or Zeros;
7.1.5 Factorization of Higher-Order Models; 7.1.6 Bode Plots for Higher-Order
Models*; 7.1.7 The Pure Delay Operator*; 7.1.8 Summary
7.2 Mechanical Vibrations 456
7.2.1 Case Study: Rotating Unbalanced Mass; 7.2.2 Case Study: Tuned Vi¬
bration Absorber; 7.2.3 Modes of Motion; 7.2.4 Case Study: Untuned Viscous
Damper; 7.2.5 Summary
7.3 Matrix Representation of Dynamic Behavior* 471
7.1.1 llie Matrix Exponential; 7.3.2 Response to a Linearly Varying Excita¬
tion; 7.3.3 Eigenvalues, Eigenvectors and Modes; 7.3.4 Case Study: Three Fluid
Tanks; 7.3.5 Case Study with Complex Roots; 7.3.6 Modified Method for Com¬
plex Eigenvalues*; 7.3.7 Case Study: Vehicle Dynamics; 7.3.8 Application of
MATLAB; 7.3.9 Response to Exponential and Frequency Excitations; 7.3.10
Representation in the s-Plane; 7.3.11 Summary
7.4 Fourier Analysis
7.4.1 Fourier Series; 7.4.2 Response of a Linear System to a Periodic Excitation;
n mat! FnTf!T; 7AA Digital SPectral Analysis*; 7.4.5 Fourier Analysis
Using MATLAB ; 7.4.6 Summary
Chapter 8 INTRODUCTION TO AUTOMATIC CONTROL 519
8.1 Open- and Closed-Loop Control 51g
Summary
XI
8.2 Dynamic Compensation 539
8.2.1 Proportional-Plus-Integral Control; 8.2.2 Proportional-Plus-Derivative
Control; 8.2.3 Proportional-Plus-Integral-Plus-Derivative Control; 8.2.4 Phase
Lead Controllers; 8.2.5 Phase Lag Controllers; 8.2.6 Phase Lead-Lag Con¬
trollers; 8.2.7 Digital Control Systems; 8.2.8 Summary
8.3 Frequency Response Methods 558
8.3.1 Polar or Nyquist Frequency Response Plots; 8.3.2 The Nyquist Stabil¬
ity Criterion; 8.3.3 Measures of Relative Stability; 8.3.4 Nichols Charts; 8.3.5
Dynamic Compensation Using Nichols Charts; 8.3.6 Approximate Correction
for Digital Sampling; 8.3.7 Special Roles for Bond Graphs in Control System
Design; 8.3.8 Summary
Chapter 9 EXTENDED MODELING 583
9.1 Modulated Transformers 583
9.1.1 Remotely Modulated Transformers; 9.1.2 Locally Modulated Transform¬
ers; 9.1.3 Increase in the Order of a Model Due to Modulation; 9.1.4 Dependent
Inertance with a Locally Modulated Transformer; 9.1.5 Inertancc Dependent
on Local Displacement; Case Study; 9.1.6 Summary
9.2 Activated Bonds 604
9.2.1 Definition and Application; 9.2.2 Causality; 9.2.3 Summary
9.3 Linear Multiport Fields 616
9.3.1 Linear Two-Port Inertance: The Electric Transformer; 9.3.2 Linear Two-
port Inertance: The Rigid Inertive Floating Link; 9.3.3 Linear Two-Port Com¬
pliance: The Piezoelectric Transducer; 9.3.4 Linear Two-Port Compliance: The
Piezomagnetic (Magnetostrictive) Transducer; 9.3.5 Linear Two-Port Compli¬
ance: The Thermoelastic Rod; 9.3.6 Linear Multiport Compliances: Gener¬
alized Linear Media*; 9.3.7 Reticulation of General Linear Multiport Fields*;
9.3.8 Summary
9.4 Nonlinear Multiport Fields 633
9.4.1 Nonlinear Compliance Fields: Generic Relationships; 9.4.2 Examples with
Geometrically Varied Capacitance; 9.4.3 Nonlinear Multiport Incrtances; 9.4.4
Inertances Dependent on Holonomic Constraints; 9.4.5 Inertances Dependent
on Nonholonomic Constraints; 9.4.6 Summary
9.5 Magnetic Circuits 651
9.5.1 Magnetic Effort, Flow and Compliance; 9.5.2 Generation of Mechanical
Forces; 9.5.3 First-Order Treatment of Permanent Magnets: A Case Study;
9.5.4 Flux Fringing and Leakage; 9.5.5 Eddy-Current Losses; 9.5.6 Saturation
and Hysteresis; 9.5.7 Simulation with Hysteresis*; 9.5.8 RC Element with Me¬
chanical Port*; 9.5.9 Summary
9.6 Electric Motors 681
9.6.1 Vector Bonds and Transformers; 9.6.2 Synchronous Motor/Brushless D.C.
Motor; 9.6.3 Three-Phase Induction Motors; 9.6.4 Single-Phase Induction Mo¬
tors; 9.6.5 Stepping Motors; 9.6.6 Summary
xii
694
9.7 Irreversible Couplers and Thermal Systems • • • ¦
9.7.1 Kffort and Flow Variables; 9.7.2 Heat Conduction; 9.7.3 The Irreversibility
Coupler; 9.7.4 Application to Friction; 9.7.5 Use of 0- and 1- Junctions, 9.7.6
Thermal Compliance; 9.7.7 Pseudo Bond Graphs for Heat Conduction, 9.7.8
Thermodynamic Coupling Between Mechanical and Thermal Energies, 9.7.9
Lead-Acid Battery: Use of Legendrc Transformation; 9.7.10 Summary
DISTRIBUTED-PARAMETER MODELS 711
Chapter 10
10
10.1.1 Camparison of Lumped and Distributed Models; 10.1.2 The Pure
.lWave Models with Simple Boundary Conditions 712
Bilateral-Wave-Delay Model; 10.1.3 Analysis of the Pure Bilateral-Wave-Delay
Model; 10.1.1 Fixed and Free Boundary Conditions; 10.1.5 Fourier Analysis
with Fixed or Free Boundary Conditions*; 10.1 6 The Hodograph Plane; 10.1.7
Summary
10.2 One-Dimensional Models 72^
10,2.1 General Formulation; 10.2.2 One-Power Models; 10.2.3 Symmetric One-
Power Models; 10.2.4 Multiple-Power Models; 10.2.5 Summary
10.3 Wave Propagation "35
10.3.1 Simplest Model: Pure Transport; 10.3.2 First Modification: Thermal
Leakage to a Constant-Temperature Environment; 10.3.3 Second Modification:
Thermal Compliance in the Walls; 10.3.4 Dispersion and Absorption; 10.3.5
Group Velocity*; 10.3.6 Summary
10.4 One-Power Symmetric Models 745
10,1.1 Wave Behavior; 10.4.2 Energy Velocity in Conservative Media*; 10.4.3
Boundary-Value Problems; Transmission Matrices; 10.4.4 Exponentially Ta¬
pered Systems*; 10.4.5 Summary
10.5 Multiple-Power Models 763
10.5.1 Symmetric and Anti-Symmetric Variables and Models; 10.5.2 Case Study
of a Degenerate System: A Counterflow Heat Exchanger; 10.5.3 Case Study of
a Symmetric Model: The Bernoulli-Euler Beam; 10.5.4 Summary
10.0 Models of Dissipative Processes 709
10.6.1 The Uniform Constant IRC Model; 10.6.2 Fluid Line Dynamics; 10.6.3
The Skin Effect in Electrical Conductors; 10.6.4 The Maxwell Model; 10.6.5
I lie Voigt. Model; 10.G.G The Linear Elastic Solid; 10.6.7 Simulation of Coupled
Storage and Dissipation Fields; 10.6.8 Example of Viscous Effects in Laminar
Flow in a Tube; 10.6.9 Example of Heat Transfer Effects in a Cylindrical Ac¬
cumulator; 10.6.10 Summary
10.7 Wave-Scattering Variables
!n7-«T,hBMr7n^i0n; 10'7'2 SinSlo-Powcr Uniform Symmetric Models;
- - he Method of Characteristics for Pure Bilateral Waves; 10 7 4 General-
rw;' N",1-Syl"m ;tiy Cases; 10.7.5 The Quasi Method of Characteristics;
Tlu- Bernoulli-Euler Beam; 10.7.7 Summary
10.8 Internal Excitation*
rs "™' sok,"°"- a,m:,
"xl *— - » ««
10.9 Modal Decomposition
815
10.9.1 General Procedure; 10.9.2 Sinusoidal Modes: Example of a Plucked
String; 10.9.3 Sinusoidal Modes: Example of a Struck Simply-Supported Beam;
10.9.4 Bond-Graph Modeling; 10.9.5 Modes with Effort-Free Boundaries: Ex¬
ample of a Bernoulli-Euler Beam; 10.9.6 Avoiding Differential Causality; 10.9.7
Summary
10.10 Complex Compound Systems: A Case Study* 832
10.10.1 A Model for Uniform Straight Tubing; 10.10.2 A Model for Uniformly
Curved Tubing; 10.10.3 The Rotation Matrix; 10.10.4 The Transmission Matrix
for a Cascade of Tubes; 10.10.5 Three-Port Junctions; 10.10.6 Added Lumped
Impedances; 10.10.7 Boundary Conditions; 10.10.8 Power Flow and Energy
Density; 10.10.9 Computational and Experimental Example; 10.10.10 Summary
Chapter 11 THERMODYNAMIC SYSTEMS 851
11.1 The Convection Bond and Compressible Flow 851
11.1.1 Flow Through a Port; 11.1.2 The Convection Bond; 11.1.3 The 125'Ele¬
ment for Fluid Flow; 11.1.4 Summary
11.2 Heat Interaction and Junctions 858
11.2.1 The Reversible Heat Interaction Element; 11.2.2 The General Heat In¬
teraction Element; 11.2.3 The HRS Macro Element; 11.2.4 The 0-Junction for
Convection Bonds; 11.2.5 Merging Streams: The OS Junction; 11.2.6 The 1-
Junction and lS-Junction with Convection; 11.2.7 Summary
11.3 Case Study with Quasi-Steady Flow* 871
11.3.1 The Bond Graph Model; 11.3.2 Irreversibilities; 11.3.3 Computation of
Results
11.4 Thermodynamic Compliance and Inertance 876
11.4.1 Application of a Simple Thermal Compliance; 11.4.2 Causality; 11.4.3
General Thermodynamic Compliance; 11.4.4 The CS'Macro Element; 11.4.5
Computations for the Ideal Gas; 11.4.6 Case Study: A Piston-Cylinder Com¬
pressor; 11.4.7 Treatment of a Quasi-Steady-State Fluid Machine; 11.4.8 Pseudo
Bond Graphs for Compressible Thermofluid Systems; 11.4.9 Fluid Inertance and
Area Change With Compressible Flow; 11.4.10 Summary
11.5 Evaluation of Thermodynamic Properties 897
11.5.1 The Most Commonly Available Analytical Form for State Properties;
11.5.2 Helmholtz Analytical Form for State Properties; 11.5.3 Application to
Gases; 11.5.4 Application to Refrigerants; 11.5.5 Application to Water; 11.5.6
Saturated Vapor Density for Other Substances; 11.5.7 Case Study: A Refriger¬
ation Cycle; 11.5.8 Application to the Liquid Region; 11.5.9 Considerations of
Reversing Flows; 11.5.10 Simulation with Fluid Kinetic Energy; 11.5.11 Heat
Transfer Equations for Three-Phase CS1 Elements; 11.5.12 Summary
11.6 Systems with Chemical Reaction* 929
11.6.1 Energy of a Pure Substance; 11.6.2 Energy of Multiple Species; 11.6.3
Stoichoimetric Coefficients and Reaction Forces; 11.6.4 Chemical Equilibrium;
11.6.5 Reaction Rates; 11.6.6 Models of Reactions without Mass Flows; 11.6.7
Models of Reactions with Mass Flows; 11.6.8 Summary
xiv
Chapter 12 TOPICS IN ADVANCED MODELING 937
937
12.1 Field Lumping.
.1.1 Scalar Fields; 12.1.2 Rigid-Body Vector Fields; 12.1.3 The Role of App¬
roximations; 12.1.4 Nodic Fields; 12.1.5 Planar Vector Nodic Fields; 12.1.6
Estimating Upper and Lower Bounds for Field Transnuttances ; 12.1.7 Three-
Dimensional Vector Nodic Fields; 12.1.8 Near-Spherical Fields; 12.1.9 Near-
Cvlindrical Fields; 12.1.10 Multiport Vector Nodic Fields; 12.1.11 Summary
955
12.2 Nonconservative Couplers
12.2.1 Causal Relations; 12.2.2 Equilibrium; 12.2.3 Dimensional Analysis; 12.2.4
Dynamic Simulation; 12.2.5 Linear Couplers; 12.2.6 Summary
12.3 Lagrange's Equations for Holonomic Systems 972
12.3.1 Primitive Coordinates and Velocities; 12.3.2 Holonomic Constraints;
12.3.3 Lagrange's Equations; 12.3.4 Example of a Solenoid; 12.3.5 Summary
12.4 Lagrangian Bond Graphs; Dissipation 981
12.4.1 Shorthand Notation; 12.4.2 Detailed Lagrangian Bond Graphs; 12.4.3
Example of the Flyball Governor; 12.4.4 Example of a Vibratory Rate Gyro;
12.4.5 Dissipation; 12.4.G Summary
12.5 Nonholonomic Constraints 988
12.5.1 Case Study: Variable-Flywheel Energy Storage for Vehicles; 12.5.2
Analysis and Representation of Nonholonomic Systems; 12.5.3 Application to
Case Study; 12.5.4 Example of the Rolling Penny; 12.5.5 Irreversible Nonholo¬
nomic Constraints; 12.5.6 The Umbra-Lagrangian of Mukherjee; 12.5.7 Sum¬
mary
12.6 Hamilton's Equations and Bond Graphs* 1000
12.6.1 Hamilton's Equations; 12.6.2 Hamiltonian Bond Graphs; 12.6.3 Applica¬
tion to Flyball Governor; 12.6.4 Example of a Seating Valve Using Lagrange's
Equations; 12.6.5 Hamilton's Equations for the Seating Valve; 12.6.6 Viscous
Dissipation; 12.6.7 Summary
APPENDIX A INTRODUCTION TO MATLAB® 1009
Scalar Calculations; Variables; Complex Numbers; Arrays and Matrices; Evalu¬
ating and Plotting Functions; Fitting Curves to Data; Control Flow Commands;
Script Files; Data Files; Function Files; Communication Between Files; MAT-
LAB Files Downloadable from the Internet
APPENDIX B CLASSICAL VIBRATIONS 1021
B.l Models with Two Degrees of Freedom 1021
B.l.l Normal Mode Vibration; B.l.2 Forced Harmonic Motion
B.2 Higher-Order Models ^3
n'n'l M0,!a! "°tioilS; B-2'2 Tho Initial Value Problem; B.2.3 Forced Response;
11.2.4 Modal Damping; B.2.5 Example Using MATLAB; B.2.6 Mode Reduction
APPENDIX C LAPLACE TRANSFORM PAIRS 1033
APPENDIX D THERMODYNAMIC DATA AND COMPUTER CODE. . 1037
D.l Programs and Data for Air and Components; D.2 Programs and Data for
Data for wLcr D'3 ^ Refrigerant R22! D4 Programs and
Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Brown, Forbes T. |
| author_facet | Brown, Forbes T. |
| author_role | aut |
| author_sort | Brown, Forbes T. |
| author_variant | f t b ft ftb |
| building | Verbundindex |
| bvnumber | BV021997450 |
| callnumber-first | T - Technology |
| callnumber-label | TA168 |
| callnumber-raw | TA168 |
| callnumber-search | TA168 |
| callnumber-sort | TA 3168 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UF 1950 ZQ 5200 |
| ctrlnum | (OCoLC)68373483 (DE-599)BVBBV021997450 |
| dewey-full | 620.001/171 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.001/171 |
| dewey-search | 620.001/171 |
| dewey-sort | 3620.001 3171 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| discipline_str_mv | Physik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021997450 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:10:58Z |
| indexdate | 2024-07-09T20:49:00Z |
| institution | BVB |
| isbn | 9780849396489 0849396484 1420009583 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015212105 |
| oclc_num | 68373483 |
| open_access_boolean | |
| owner | DE-706 DE-634 DE-83 DE-573 |
| owner_facet | DE-706 DE-634 DE-83 DE-573 |
| physical | XIX, 1058 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | CRC, Taylor & Francis |
| record_format | marc |
| spelling | Brown, Forbes T. Verfasser aut Engineering system dynamics a unified graph-centered approach 2. ed. Boca Raton, FL [u.a.] CRC, Taylor & Francis 2007 XIX, 1058 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bond graphs Dynamics Engineering models Systems engineering Dynamisches System (DE-588)4013396-5 gnd rswk-swf Regelungssystem (DE-588)4134712-2 gnd rswk-swf Bondgraph (DE-588)4238912-4 gnd rswk-swf Bondgraph (DE-588)4238912-4 s DE-604 Dynamisches System (DE-588)4013396-5 s Regelungssystem (DE-588)4134712-2 s 1\p DE-604 http://www.loc.gov/catdir/enhancements/fy0661/2006045235-d.html Beschreibung für Leser HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015212105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brown, Forbes T. Engineering system dynamics a unified graph-centered approach Bond graphs Dynamics Engineering models Systems engineering Dynamisches System (DE-588)4013396-5 gnd Regelungssystem (DE-588)4134712-2 gnd Bondgraph (DE-588)4238912-4 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4134712-2 (DE-588)4238912-4 |
| title | Engineering system dynamics a unified graph-centered approach |
| title_auth | Engineering system dynamics a unified graph-centered approach |
| title_exact_search | Engineering system dynamics a unified graph-centered approach |
| title_exact_search_txtP | Engineering system dynamics a unified graph-centered approach |
| title_full | Engineering system dynamics a unified graph-centered approach |
| title_fullStr | Engineering system dynamics a unified graph-centered approach |
| title_full_unstemmed | Engineering system dynamics a unified graph-centered approach |
| title_short | Engineering system dynamics |
| title_sort | engineering system dynamics a unified graph centered approach |
| title_sub | a unified graph-centered approach |
| topic | Bond graphs Dynamics Engineering models Systems engineering Dynamisches System (DE-588)4013396-5 gnd Regelungssystem (DE-588)4134712-2 gnd Bondgraph (DE-588)4238912-4 gnd |
| topic_facet | Bond graphs Dynamics Engineering models Systems engineering Dynamisches System Regelungssystem Bondgraph |
| url | http://www.loc.gov/catdir/enhancements/fy0661/2006045235-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015212105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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