Introduction to Dynamic System Analysis

Cover
Contents
Preface
1. Introduction
2. Writing Differential Equations
2-1. Introduction
2-2. Mechanical Systems
2-3. Hydraulic Systems
2-4. Electric Systems
2-5. A Thermal System
2-6. An Ecological System
2-7. A Political-Military System
2-8. Conclusion
Problems
3. Solving Differential Equations
3-1. Introduction
3-2. Solution of Homogeneous Equations
3-3. Consideration of Initial Conditions
3-4. Solution of Nonhomogeneous Equations
3-5. Transient and Steady-State Responses
3-6. Combining Simultaneous Equations
3-7. Conclusion
Problems
4. Linear Equations for Modeling Nonlinear Systems
4-1. Introduction
4-2. Examples of Nonlinearities
4-3. Principles of Linearization
4-4. Conclusion
Problems
5. Introduction to Vibrations
5-1. Introductions
5-2. Basic Principles and Definitions
5-3. Units
5-4. Conclusion
Problems
6. Free Vibration: Systems with a Single Degree of Freedom
6-1. Introduction
6-2. Undamped Free Vibration
6-3. Damped Free Vibration
6-4. Determination of Damping Ratio from Experimental Data
6-5. Conclusion
Problems
7. Forced Vibration: Systems with a Single Degree of Freedom
7-1. Introduction
7-2. Examples of Mechanical Vibrating Systems with Sinusoidal Inputs
7-3. Frequency Response
7-4. Vibration Caused by Rotating Unbalance
7-5. Displacement Input Acting Through a Dashpot and Spring in Parallel
7-6. Transmissibility
7-7. Systems with Simultaneous Inputs at Two or More Frequencies
7-8. Conclusion
Problems
8. More Complex Single-Degree-of-Freedom Systems
8-1. Introduction
8-2. Determining the Degrees of Freedom of a Mechanical System
8-3. Method of Analysis
8-4. Equivalent Inertia, Damping, and Spring Rate
8-5. Conclusion
Problems
9. Vibrating Systems with More Than One Degree of Freedom
9-1. Introduction
9-2. Writing the Equations of Motion
9-3. Two-Mass System Without Damping
9-4. Two-Mass System with Damping
9-5. Vibrating Systems with More Than Two Degrees of Freedom
9-6. Conclusion
Problems
10. DIstributed Parameter Systems
10-1. Introduction
10-2. Rigorous Analysis of a Distributed Parameter System
10-3. Beams with Other Boundary Conditions
10-4. Conclusion
Problems
11. Critical Speeds of Rotors
11-1. Introduction
11-2. Analysis of a Simple Lumped Parameter Rotor
11-3. Effect of Compliance in Bearings and Bearing Mounts
11-4. Other Critical Speed Considerations
11-5. Similar Rotor Instability Phenomena
11-6. Conclusion
Problems
12. Balance of Rotors
12-1. Introduction
12-2. Static Balance
12-3. Dynamic Balance
12-4. Conclusion
Problems
13. The Feedback Control System
13-1. Introduction
13-2. Home Heating Application
13-3. Feedback Control Systems
13-4. Conclusion
14. System Response and Stability
14-1. Introduction
14-2. Response of a Liquid-Level System
14-3. First-Order System Response to a Step Input
14-4. First-Order System Response to a Sinusoidal Input
14-5. Second-Order System Response
14-6. Response of Higher-Order Systems to Simple Sinusoidal Inputs
14-7. The Concept of System Stability
14-8. Conclusion
Problems
15. Control Actions
15-1. Introduction
15-2. Proportional Control
15-3. Integral Control
15-4. Proportional-plus-Integral Control
15-5. "Bang-Bang" Control
15-6. Other Control Actions
15-7. Conclusion
Problems
16. Block Diagrams
16-1. Introduction
16-2. The Transfer Function
16-3. The Block Diagram
16-4. Block Diagram Algebra
16-5. Liquid-Level Integral Control System Example
16-6. Systems with Two or More Inputs
16-7. Feedback Compensation
16-8. Conclusion
Problems
17. State-Variable Formulation and Computer Solutions
17-1. Introduction
17-2. State-Variable Formulation
17-3. State-Space Trajectories
17-4. Analog Computer Solutions
17-5. Digital Computer Solutions
17-6. Conclusion
Problems
18. Experimental Determination of System Dynamic Characteristics
18-1. Introduction
18-2. Test Equipment and Instrumentation
18-3. Applying System Inputs
18-4. Recording and Interpreting System Response
18-5. Conclusion
Problems
Appendix A. Deflection of Beams
Appendix B. Alternative Mathematical Expressions for Certain Harmonic Functions
Appendix C. Solution of Equations
Appendix D. Steady-State Solutions by Rotating-Vector and Comples-Number Techniques
Appendix E. Rayleigh's Energy Method
Appendix F. Decibel Conversion Table
Appendix G. Routh's Criterion
Bibliography
Index