Vibration with Control

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.

Author Notes

Daniel J. Inman , University of Michigan, USA

Preface	p. xi
About the Companion Website	p. xiii
1 Single Degree of Freedom Systems	p. 1
1.1 Introduction	p. 1
1.2 Spring-Mass System	p. 1
1.3 Spring-Mass-Damper System	p. 6
1.4 Forced Response	p. 10
1.5 Transfer Functions and Frequency Methods	p. 17
1.6 Complex Representation and Impedance	p. 23
1.7 Measurement and Testing	p. 25
1.8 Stability	p. 28
1.9 Design and Control of Vibrations	p. 31
1.10 Nonlinear Vibrations	p. 35
1.11 Computing and Simulation in MATLAB™	p. 38
Chapter Notes	p. 43
References	p. 44
Problems	p. 46
2 Lumped Parameter Models	p. 49
2.1 Introduction	p. 49
2.2 Modeling	p. 52
2.3 Classifications of Systems	p. 56
2.4 Feedback Control Systems	p. 57
2.5 Examples	p. 59
2.6 Experimental Models	p. 64
2.7 Nonlinear Models and Equilibrium	p. 65
Chapter Notes	p. 67
References	p. 68
Problems	p. 68
3 Matrices and the Free Response	p. 71
3.1 Introduction	p. 71
3.2 Eigenvalues and Eigenvectors	p. 71
3.3 Natural Frequencies and Mode Shapes	p. 77
3.4 Canonical Forms	p. 86
3.5 Lambda Matrices	p. 91
3.6 Eigenvalue Estimates	p. 94
3.7 Computation Eigenvalue Problems in MATLAB	p. 101
3.8 Numerical Simulation of the Time Response in MATLAB™	p. 104
Chapter Notes	p. 106
References	p. 107
Problems	p. 108
4 Stability	p. 113
4.1 Introduction	p. 113
4.2 Lyapunov Stability	p. 113
4.3 Conservative Systems	p. 116
4.4 Systems with Damping	p. 117
4.5 Semidefinite Damping	p. 118
4.6 Gyroscopic Systems	p. 119
4.7 Damped Gyroscopic Systems	p. 121
4.8 Circulatory Systems	p. 122
4.9 Asymmetric Systems	p. 123
4.10 Feedback Systems	p. 128
4.11 Stability in the State Space	p. 131
4.12 Stability of Nonlinear Systems	p. 133
Chapter Notes	p. 137
References	p. 138
Problems	p. 139
5 Forced Response of Lumped Parameter Systems	p. 143
5.1 Introduction	p. 143
5.2 Response via State Space Methods	p. 143
5.3 Decoupling Conditions and Modal Analysis	p. 148
5.4 Response of Systems with Damping	p. 152
5.5 Stability of the Forced Response	p. 155
5.6 Response Bounds	p. 157
5.7 Frequency Response Methods	p. 158
5.8 Stability of Feedback Control	p. 161
5.9 Numerical Simulations in MATLAB	p. 163
Chapter Notes	p. 165
References	p. 166
Problems	p. 167
6 Vibration Suppression	p. 171
6.1 Introduction	p. 171
6.2 Isolators and Absorbers	p. 172
6.3 Optimization Methods	p. 175
6.4 Metastructures	p. 179
6.5 Design Sensitivity and Redesign	p. 181
6.6 Passive and Active Control	p. 184
6.7 Controllability and Observability	p. 188
6.8 Eigenstructure Assignment	p. 193
6.9 Optimal Control	p. 196
6.10 Observers (Estimators)	p. 203
6.11 Realization	p. 208
6.12 Reduced-Order Modeling	p. 210
6.13 Modal Control in State Space	p. 216
6.14 Modal Control in Physical Space	p. 219
6.15 Robustness	p. 224
6.16 Positive Position Feedback Control	p. 226
6.17 MATLAB Commands for Control Calculations	p. 229
Chapter Notes	p. 233
References	p. 234
Problems	p. 237
7 Distributed Parameter Models	p. 241
7.1 Introduction	p. 241
7.2 Equations of Motion	p. 241
7.3 Vibration of Strings	p. 247
7.4 Rods and Bars	p. 252
7.5 Vibration of Beams	p. 256
7.6 Coupled Effects	p. 263
7.7 Membranes and Plates	p. 267
7.8 Layered Materials	p. 271
7.9 Damping Models	p. 273
7.10 Modeling Piezoelectric Wafers	p. 276
Chapter Notes	p. 281
References	p. 281
Problems	p. 283
8 Formal Methods of Solutions	p. 287
8.1 Introduction	p. 287
8.2 Boundary Value Problems and Eigenfunctions	p. 287
8.3 Modal Analysis of the Free Response	p. 290
8.4 Modal Analysis in Damped Systems	p. 292
8.5 Transform Methods	p. 294
8.6 Green's Functions	p. 296
Chapter Notes	p. 300
References	p. 301
Problems	p. 301
9 Operators and the Free Response	p. 303
9.1 Introduction	p. 303
9.2 Hilbert Spaces	p. 304
9.3 Expansion Theorems	p. 308
9.4 Linear Operators	p. 309
9.5 Compact Operators	p. 315
9.6 Theoretical Modal Analysis	p. 317
9.7 Eigenvalue Estimates	p. 318
9.8 Enclosure Theorems	p. 321
Chapter Notes	p. 324
References	p. 324
Problems	p. 325
10 Forced Response and Control	p. 327
10.1 Introduction	p. 327
10.2 Response by Modal Analysis	p. 327
10.3 Modal Design Criteria	p. 330
10.4 Combined Dynamical Systems	p. 332
10.5 Passive Control and Design	p. 336
10.6 Distributed Modal Control	p. 338
10.7 Nonmodal Distributed Control	p. 340
10.8 State Space Control Analysis	p. 341
10.9 Vibration Suppression using Piezoelectric Materials	p. 342
Chapter Notes	p. 344
References	p. 345
Problems	p. 346
11 Approximations of Distributed Parameter Models	p. 349
11.1 Introduction	p. 349
11.2 Modal Truncation	p. 349
11.3 Rayleigh-Ritz-Galerkin Approximations	p. 351
11.4 Finite Element Method	p. 354
11.5 Substructure Analysis	p. 359
11.6 Truncation in the Presence of Control	p. 361
11.7 Impedance Method of Truncation and Control	p. 369
Chapter Notes	p. 371
References	p. 371
Problems	p. 372
12 Vibration Measurement	p. 375
12.1 Introduction	p. 375
12.2 Measurement Hardware	p. 376
12.3 Digital Signal Processing	p. 379
12.4 Random Signal Analysis	p. 383
12.5 Modal Data Extraction (Frequency Domain)	p. 387
12.6 Modal Data Extraction (Time Domain)	p. 390
12.7 Model Identification	p. 395
12.3 Model Updating	p. 397
12.9 Verification and Validation	p. 398
Chapter Notes	p. 400
References	p. 401
Problems	p. 402
A Comments on Units	p. 405
B Supplementary Mathematics	p. 409
Index	p. 413

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