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More About This Title Vibration with Control
English
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 controlIntroduces the use of Matlab into the solution of vibration and vibration control problemsProvides a unique blend of practical and theoretical developmentsContains examples and problems along with a solutions manual and power point presentationsVibration 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.
English
English
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
