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.

Table of Contents:
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 References 281 Problems 283 8 Formal Methods of Solutions 287 8.1 Introduction 287 8.2 Boundary Value Problems and Eigenfunctions 287 8.3 Modal Analysis of the Free Response 290 8.4 Modal Analysis in Damped Systems 292 8.5 Transform Methods 294 8.6 Green’s Functions 296 Chapter Notes 300 References 301 Problems 301 9 Operators and the Free Response 303 9.1 Introduction 303 9.2 Hilbert Spaces 304 9.3 Expansion Theorems 308 9.4 Linear Operators 309 9.5 Compact Operators 315 9.6 Theoretical Modal Analysis 317 9.7 Eigenvalue Estimates 318 9.8 Enclosure Theorems 321 Chapter Notes 324 References 324 Problems 325 10 Forced Response and Control 327 10.1 Introduction 327 10.2 Response by Modal Analysis 327 10.3 Modal Design Criteria 330 10.4 Combined Dynamical Systems 332 10.5 Passive Control and Design 336 10.6 Distributed Modal Control 338 10.7 Nonmodal Distributed Control 340 10.8 State Space Control Analysis 341 10.9 Vibration Suppression using Piezoelectric Materials 342 Chapter Notes 344 References 345 Problems 346 11 Approximations of Distributed Parameter Models 349 11.1 Introduction 349 11.2 Modal Truncation 349 11.3 Rayleigh-Ritz-Galerkin Approximations 351 11.4 Finite Element Method 354 11.5 Substructure Analysis 359 11.6 Truncation in the Presence of Control 361 11.7 Impedance Method of Truncation and Control 369 Chapter Notes 371 References 371 Problems 372 12 Vibration Measurement 375 12.1 Introduction 375 12.2 Measurement Hardware 376 12.3 Digital Signal Processing 379 12.4 Random Signal Analysis 383 12.5 Modal Data Extraction (Frequency Domain) 387 12.6 Modal Data Extraction (Time Domain) 390 12.7 Model Identification 395 12.8 Model Updating 397 12.9 Verification and Validation 398 Chapter Notes 400 References 401 Problems 402 A Comments on Units 405 B Supplementary Mathematics 409 Index 413