Vibration with Control

An advanced look at vibration analysis with a focus on active vibration suppression

As modern devices, from cell phones to airplanes, become lighter and more flexible, vibration suppression and analysis becomes more critical. Vibration with Control, 2nd Edition includes modelling, analysis and testing methods. New topics include metastructures and the use of piezoelectric materials, and numerical methods are also discussed. All material is placed on a firm mathematical footing by introducing concepts from linear algebra (matrix theory) and applied functional analysis when required.

Key features:

• Combines vibration modelling and analysis with active control to provide concepts for effective vibration suppression.

• Introduces the use of piezoelectric materials for vibration sensing and suppression.

• Provides a unique blend of practical and theoretical developments.

• Examines nonlinear as well as linear vibration analysis.

• Provides Matlab instructions for solving problems.

• Contains examples and problems.

• PowerPoint Presentation materials and digital solutions manual available for instructors.

Vibration with Control, 2nd Edition is an ideal reference and textbook for graduate students in mechanical, aerospace and structural engineering, as well as researchers and practitioners in the field.

Autorentext

Daniel J. Inman, University of Michigan, USA

Inhalt

Preface xi

About the Companion Website xiii

1 Single Degree of Freedom Systems 1

1.1 Introduction 1

1.2 Spring-Mass System 1

1.3 Spring-Mass-Damper System 6

1.4 Forced Response 10

1.5 Transfer Functions and Frequency Methods 17

1.6 Complex Representation and Impedance 23

1.7 Measurement and Testing 25

1.8 Stability 28

1.9 Design and Control of Vibrations 31

1.10 Nonlinear Vibrations 35

1.11 Computing and Simulation in MatlabTM 38

Chapter Notes 43

References 44

Problems 46

2 Lumped Parameter Models 49

2.1 Introduction 49

2.2 Modeling 52

2.3 Classifications of Systems 56

2.4 Feedback Control Systems 57

2.5 Examples 59

2.6 Experimental Models 64

2.7 Nonlinear Models and Equilibrium 65

Chapter Notes 67

References 68

Problems 68

3 Matrices and the Free Response 71

3.1 Introduction 71

3.2 Eigenvalues and Eigenvectors 71

3.3 Natural Frequencies and Mode Shapes 77

3.4 Canonical Forms 86

3.5 Lambda Matrices 91

3.6 Eigenvalue Estimates 94

3.7 Computation Eigenvalue Problems in MATLAB 101

3.8 Numerical Simulation of the Time Response in MATLABtm 104

Chapter Notes 106

References 107

Problems 108

4 Stability 113

4.1 Introduction 113

4.2 Lyapunov Stability 113

4.3 Conservative Systems 116

4.4 Systems with Damping 117

4.5 Semidefinite Damping 118

4.6 Gyroscopic Systems 119

4.7 Damped Gyroscopic Systems 121

4.8 Circulatory Systems 122

4.9 Asymmetric Systems 123

4.10 Feedback Systems 128

4.11 Stability in the State Space 131

4.12 Stability of Nonlinear Systems 133

Chapter Notes 137

References 138

Problems 139

5 Forced Response of Lumped Parameter Systems 143

5.1 Introduction 143

5.2 Response via State SpaceMethods 143

5.3 Decoupling Conditions and Modal Analysis 148

5.4 Response of Systems with Damping 152

5.5 Stability of the Forced Response 155

5.6 Response Bounds 157

5.7 Frequency Response Methods 158

5.8 Stability of Feedback Control 161

5.9 Numerical Simulations in Matlab 163

Chapter Notes 165

References 166

Problems 167

6 Vibration Suppression 171

6.1 Introduction 171

6.2 Isolators and Absorbers 172

6.3 OptimizationMethods 175

6.4 Metastructures 179

6.5 Design Sensitivity and Redesign 181

6.6 Passive and Active Control 184

6.7 Controllability and Observability 188

6.8 Eigenstructure Assignment 193

6.9 Optimal Control 196

6.10 Observers (Estimators) 203

6.11 Realization 208

6.12 Reduced-Order Modeling 210

6.13 Modal Control in State Space 216

6.14 Modal Control in Physical Space 219

6.15 Robustness 224

6.16 Positive Position Feedback Control 226

6.17 Matlab Commands for Control Calculations 229

Chapter Notes 233

References 234

Problems 237

7 Distributed Parameter Models 241

7.1 Introduction 241

7.2 Equations of Motion 241

7.3 Vibration of Strings 247

7.4 Rods and Bars 252

7.5 Vibration of Beams 256

7.6 Coupled Effects 263

7.7 Membranes and Plates 267

7.8 Layered Materials 271

7.9 Damping Models 273

7.10 Modeling Piezoelectric Wafers 276

Chapter Notes 281 <p&gt...