Vibration with Control

Engineers are becoming increasingly aware of the problems caused by vibration in engineering design, particularly in the areas of structural health monitoring and smart structures. Vibration is a constant problem as it can impair performance and lead to fatigue, damage and the failure of a structure. Control of vibration is a key factor in preventing such detrimental results. This book presents a homogenous treatment of vibration by including those factors from control that are relevant to modern vibration analysis, design and measurement. Vibration and control are established on a firm mathematical basis and the disciplines of vibration, control, linear algebra, matrix computations, and applied functional analysis are connected. Key Features: Assimilates the discipline of contemporary structural vibration with active control Introduces the use of Matlab into the solution of vibration and vibration control problems Provides a unique blend of practical and theoretical developments Contains examples and problems along with a solutions manual and power point presentations Vibration with Control is an essential text for practitioners, researchers, and graduate students as it can be used as a reference text for its complex chapters and topics, or in a tutorial setting for those improving their knowledge of vibration and learning about control for the first time. Whether or not you are familiar with vibration and control, this book is an excellent introduction to this emerging and increasingly important engineering discipline.

Table of Contents:
Preface xi 1 Single-degree-of-freedom Systems 1 1.1 Introduction 1 1.2 Spring–Mass System 1 1.3 Spring–Mass–Damper System 4 1.4 Forced Response 8 1.5 Transfer Functions and Frequency Methods 14 1.6 Measurement and Testing 19 1.7 Stability 22 1.8 Design and Control of Vibrations 24 1.9 Nonlinear Vibrations 27 1.10 Computing and Simulation in Matlab 29 Chapter Notes 35 References 35 Problems 36 2 Lumped-parameter Models 39 2.1 Introduction 39 2.2 Classifications of Systems 42 2.3 Feedback Control Systems 44 2.4 Examples 45 2.5 Experimental Models 49 2.6 Influence Methods 50 2.7 Nonlinear Models and Equilibrium 52 Chapter Notes 54 References 55 Problems 55 3 Matrices and the Free Response 57 3.1 Introduction 57 3.2 Eigenvalues and Eigenvectors 58 3.3 Natural Frequencies and Mode Shapes 63 3.4 Canonical Forms 71 3.5 Lambda Matrices 74 3.6 Oscillation Results 77 3.7 Eigenvalue Estimates 81 3.8 Computation Eigenvalue Problems in Matlab 88 3.9 Numerical Simulation of the Time Response in Matlab 91 Chapter Notes 93 References 94 Problems 95 4 Stability 99 4.1 Introduction 99 4.2 Lyapunov Stability 99 4.3 Conservative Systems 101 4.4 Systems with Damping 103 4.5 Semidefinite Damping 103 4.6 Gyroscopic Systems 104 4.7 Damped Gyroscopic Systems 106 4.8 Circulatory Systems 107 4.9 Asymmetric Systems 109 4.10 Feedback Systems 113 4.11 Stability in State Space 116 4.12 Stability Boundaries 118 Chapter Notes 119 References 120 Problems 121 5 Forced Response of Lumped-parameter Systems 123 5.1 Introduction 123 5.2 Response via State-space Methods 123 5.3 Decoupling Conditions and Modal Analysis 128 5.4 Response of Systems with Damping 132 5.5 Bounded-input, Bounded-output Stability 134 5.6 Response Bounds 136 5.7 Frequency Response Methods 138 5.8 Numerical Simulation in Matlab 140 Chapter Notes 142 References 142 Problems 143 6 Design Considerations 145 6.1 Introduction 145 6.2 Isolators and Absorbers 145 6.3 Optimization Methods 148 6.4 Damping Design 153 6.5 Design Sensitivity and Redesign 155 6.6 Passive and Active Control 158 6.7 Design Specifications 160 6.8 Model Reduction 161 Chapter Notes 164 References 165 Problems 165 7 Control of Vibrations 169 7.1 Introduction 169 7.2 Controllability and Observability 171 7.3 Eigenstructure Assignment 176 7.4 Optimal Control 179 7.5 Observers (Estimators) 185 7.6 Realization 190 7.7 Reduced-order Modeling 192 7.8 Modal Control in State Space 198 7.9 Modal Control in Physical Space 202 7.10 Robustness 206 7.11 Positive Position Feedback 208 7.12 Matlab Commands for Control Calculations 211 Chapter Notes 216 References 217 Problems 218 8 Modal Testing 221 8.1 Introduction 221 8.2 Measurement Hardware 222 8.3 Digital Signal Processing 225 8.4 Random Signal Analysis 229 8.5 Modal Data Extraction (Frequency Domain) 232 8.6 Modal Data Extraction (Time Domain) 235 8.7 Model Identification 241 8.8 Model Updating 243 Chapter Notes 244 References 245 Problems 246 9 Distributed-parameter Models 249 9.1 Introduction 249 9.2 Vibration of Strings 249 9.3 Rods and Bars 256 9.4 Vibration of Beams 260 9.5 Membranes and Plates 264 9.6 Layered Materials 268 9.7 Viscous Damping 270 Chapter Notes 271 References 272 Problems 273 10 Formal Methods of Solution 275 10.1 Introduction 275 10.2 Boundary Value Problems and Eigenfunctions 275 10.3 Modal Analysis of the Free Response 278 10.4 Modal Analysis in Damped Systems 280 10.5 Transform Methods 282 10.6 Green’s Functions 284 Chapter Notes 288 References 289 Problems 289 11 Operators and the Free Response 291 11.1 Introduction 291 11.2 Hilbert Spaces 291 11.3 Expansion Theorems 296 11.4 Linear Operators 297 11.5 Compact Operators 303 11.6 Theoretical Modal Analysis 304 11.7 Eigenvalue Estimates 306 11.8 Enclosure Theorems 308 11.9 Oscillation Theory 310 Chapter Notes 312 References 313 Problems 313 12 Forced Response and Control 315 12.1 Introduction 315 12.2 Response by Modal Analysis 315 12.3 Modal Design Criteria 318 12.4 Combined Dynamical Systems 320 12.5 Passive Control and Design 324 12.6 Distributed Modal Control 326 12.7 Nonmodal Distributed Control 328 12.8 State-space Control Analysis 329 Chapter Notes 330 References 331 Problems 332 13 Approximations of Distributed-parameter Models 333 13.1 Introduction 333 13.2 Modal Truncation 333 13.3 Rayleigh–Ritz–Galerkin Approximations 335 13.4 Finite Element Method 337 13.5 Substructure Analysis 342 13.6 Truncation in the Presence of Control 345 13.7 Impedance Method of Truncation and Control 352 Chapter Notes 354 References 355 Problems 355 A Comments on Units 357 B Supplementary Mathematics 361 Index 365

About the Author :
Daniel J. Inman; Director, Center for Intelligent Material Systems and Structures, 310 Durham Hall, Mail Code 0261, Virginia Tech, Blacksburg, VA 24061 USA Since 1980, he has published five books (on vibration, control, statics, and dynamics), eight software manuals, seven book chapters, over 160 journal papers and 300 proceedings papers, graduated 35 Ph.D. students and supervised more than 55 MS degrees. He is currently Technical Editor of the Journal of Intelligent Material Systems and Structures (1999-2004), Technical Editor of the Shock and Vibration Digest (1998-2001), and Technical Editor of the journal Shock and Vibration (1999-2004).