Vibration with Control

Daniel J. Inman, University of Michigan, USA

• Preface xiAbout the Companion Website xiii1 Single Degree of Freedom Systems 11.1 Introduction 11.2 Spring-Mass System 11.3 Spring-Mass-Damper System 61.4 Forced Response 101.5 Transfer Functions and Frequency Methods 171.6 Complex Representation and Impedance 231.7 Measurement and Testing 251.8 Stability 281.9 Design and Control of Vibrations 311.10 Nonlinear Vibrations 351.11 Computing and Simulation in MatlabTM 38Chapter Notes 43References 44Problems 462 Lumped Parameter Models 492.1 Introduction 492.2 Modeling 522.3 Classifications of Systems 562.4 Feedback Control Systems 572.5 Examples 592.6 Experimental Models 642.7 Nonlinear Models and Equilibrium 65Chapter Notes 67References 68Problems 683 Matrices and the Free Response 713.1 Introduction 713.2 Eigenvalues and Eigenvectors 713.3 Natural Frequencies and Mode Shapes 773.4 Canonical Forms 863.5 Lambda Matrices 913.6 Eigenvalue Estimates 943.7 Computation Eigenvalue Problems in MATLAB 1013.8 Numerical Simulation of the Time Response in MATLABtm 104Chapter Notes 106References 107Problems 1084 Stability 1134.1 Introduction 1134.2 Lyapunov Stability 1134.3 Conservative Systems 1164.4 Systems with Damping 1174.5 Semidefinite Damping 1184.6 Gyroscopic Systems 1194.7 Damped Gyroscopic Systems 1214.8 Circulatory Systems 1224.9 Asymmetric Systems 1234.10 Feedback Systems 1284.11 Stability in the State Space 1314.12 Stability of Nonlinear Systems 133Chapter Notes 137References 138Problems 1395 Forced Response of Lumped Parameter Systems 1435.1 Introduction 1435.2 Response via State SpaceMethods 1435.3 Decoupling Conditions and Modal Analysis 1485.4 Response of Systems with Damping 1525.5 Stability of the Forced Response 1555.6 Response Bounds 1575.7 Frequency Response Methods 1585.8 Stability of Feedback Control 1615.9 Numerical Simulations in Matlab 163Chapter Notes 165References 166Problems 1676 Vibration Suppression 1716.1 Introduction 1716.2 Isolators and Absorbers 1726.3 OptimizationMethods 1756.4 Metastructures 1796.5 Design Sensitivity and Redesign 1816.6 Passive and Active Control 1846.7 Controllability and Observability 1886.8 Eigenstructure Assignment 1936.9 Optimal Control 1966.10 Observers (Estimators) 2036.11 Realization 2086.12 Reduced-Order Modeling 2106.13 Modal Control in State Space 2166.14 Modal Control in Physical Space 2196.15 Robustness 2246.16 Positive Position Feedback Control 2266.17 Matlab Commands for Control Calculations 229Chapter Notes 233References 234Problems 2377 Distributed Parameter Models 2417.1 Introduction 2417.2 Equations of Motion 2417.3 Vibration of Strings 2477.4 Rods and Bars 2527.5 Vibration of Beams 2567.6 Coupled Effects 2637.7 Membranes and Plates 2677.8 Layered Materials 2717.9 Damping Models 2737.10 Modeling Piezoelectric Wafers 276Chapter Notes 281References 281Problems 2838 Formal Methods of Solutions 2878.1 Introduction 2878.2 Boundary Value Problems and Eigenfunctions 2878.3 Modal Analysis of the Free Response 2908.4 Modal Analysis in Damped Systems 2928.5 Transform Methods 2948.6 Green’s Functions 296Chapter Notes 300References 301Problems 3019 Operators and the Free Response 3039.1 Introduction 3039.2 Hilbert Spaces 3049.3 Expansion Theorems 3089.4 Linear Operators 3099.5 Compact Operators 3159.6 Theoretical Modal Analysis 3179.7 Eigenvalue Estimates 3189.8 Enclosure Theorems 321Chapter Notes 324References 324Problems 32510 Forced Response and Control 32710.1 Introduction 32710.2 Response by Modal Analysis 32710.3 Modal Design Criteria 33010.4 Combined Dynamical Systems 33210.5 Passive Control and Design 33610.6 Distributed Modal Control 33810.7 Nonmodal Distributed Control 34010.8 State Space Control Analysis 34110.9 Vibration Suppression using Piezoelectric Materials 342Chapter Notes 344References 345Problems 34611 Approximations of Distributed Parameter Models 34911.1 Introduction 34911.2 Modal Truncation 34911.3 Rayleigh-Ritz-Galerkin Approximations 35111.4 Finite Element Method 35411.5 Substructure Analysis 35911.6 Truncation in the Presence of Control 36111.7 Impedance Method of Truncation and Control 369Chapter Notes 371References 371Problems 37212 Vibration Measurement 37512.1 Introduction 37512.2 Measurement Hardware 37612.3 Digital Signal Processing 37912.4 Random Signal Analysis 38312.5 Modal Data Extraction (Frequency Domain) 38712.6 Modal Data Extraction (Time Domain) 39012.7 Model Identification 39512.8 Model Updating 39712.9 Verification and Validation 398Chapter Notes 400References 401Problems 402A Comments on Units 405B Supplementary Mathematics 409Index 413