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Vibration with Control

ISBN: 978-0-470-01051-8
388 pages
August 2006
Vibration with Control (0470010517) cover image

Description

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.

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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

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Author Information

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).
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