Introduction to Dynamic System Analysis

Description

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