Complete guide to signal processing and modal analysis theory, with coverage of practical applications and a plethora of learning tools
Featuring numerous line diagrams and illustrations, the newly revised and updated Second Edition of Noise and Vibration Analysis is a comprehensive and practical guide that combines both signal processing and modal analysis theory with their practical application in noise and vibration analysis. This new edition has been updated with three new chapters covering experimental modal analysis, operational modal analysis, and practical vibration measurements.
Taking a practical learning approach, the text includes exercises that allow the content to be developed in an academic course framework or as supplementary material for private and further study, including multiple choice questions at the end of each chapter. An accompanying website hosts a MATLAB® toolbox, additional problems and examples, and videos.
Written by a highly qualified author with significant experience in the field, Noise and Vibration Analysis covers topics such as: - Dynamic signals and systems, covering periodic, random, and transient signals, RMS value and power, and the Continuous Fourier Transform - Time data analysis, covering the sampling theorem, analog, digital, smoothing, and acoustic octave filters, time data differentiation, and FFT-based processing - Statistics and random processes, covering expected value, errors in estimates, and probability distribution in random theory, and tests of normality and stationarity - Fundamental mechanics, covering Newton’s laws, alternative quantities for describing motion, frequency response plot formats, and rotating mass
Noise and Vibration Analysis is an excellent resource for researchers and engineers from the automotive, aerospace, mechanical, or electronics industries who work with experimental or analytical vibration analysis and/or acoustics. The text is also valuable for graduate students enrolled in vibration analysis, experimental structural dynamics, or applied signal analysis courses.
Table of Contents
About the Author xix
Preface xxi
Acknowledgments xxv
List of Abbreviations xxvii
Annotation xxix
1 Introduction 1
1.1 Noise and Vibration 1
1.2 Noise and Vibration Analysis 2
1.3 Application Areas 3
1.4 Analysis of Noise and Vibrations 4
1.5 Standards 5
1.6 Becoming a Noise and Vibration Analysis Expert 5
2 Dynamic Signals and Systems 9
2.1 Introduction 9
2.2 Periodic Signals 11
2.3 Random Signals 16
2.4 Transient Signals 17
2.5 RMS Value and Power 18
2.6 Linear Systems 19
2.7 The Continuous Fourier Transform 29
2.8 Chapter Summary 35
2.9 Problems 36
References 38
3 Time Data Analysis 39
3.1 Introduction to Discrete Signals 39
3.2 The Sampling Theorem 40
3.3 Filters 48
3.4 Time Series Analysis 57
3.5 Chapter Summary 66
3.6 Problems 67
References 68
4 Statistics and Random Processes 71
4.1 Introduction to the Use of Statistics 71
4.2 Random Theory 73
4.3 Statistical Methods 83
4.4 Quality Assessment of Measured Signals 91
4.5 Chapter Summary 94
4.6 Problems 95
References 96
5 Fundamental Mechanics 97
5.1 Newton’s Laws 97
5.2 The Single Degree-of-Freedom System (SDOF) 98
5.3 Alternative Quantities for Describing Motion 106
5.4 Frequency Response Plot Formats 108
5.5 Determining Natural Frequency and Damping Ratio 113
5.6 Rotating Mass 115
5.7 Some Comments on Damping 116
5.8 Models Based on SDOF Approximations 118
5.9 The Two Degree of Freedom System (2DOF) 121
5.10 The Tuned Damper 123
5.11 Chapter Summary 125
5.12 Problems 126
References 127
6 Modal Analysis Theory 129
6.1 Waves on a String 129
6.2 Matrix Formulations 131
6.3 Eigenvalues and Eigenvectors 132
6.4 Frequency Response of MDOF Systems 146
6.5 Free Decays 155
6.6 Chapter Summary 156
6.7 Problems 157
References 158
7 Transducers for Noise and Vibration Analysis 159
7.1 The Piezoelectric Effect 159
7.2 The Charge Amplifier 160
7.3 Transducers with Built-In Impedance Converters, “IEPE” 162
7.4 The Piezoelectric Accelerometer 165
7.5 The Piezoelectric Force Transducer 170
7.6 The Impedance Head 171
7.7 The Impulse Hammer 172
7.8 Accelerometer Calibration 173
7.9 Measurement Microphones 174
7.10 Microphone Calibration 175
7.11 The Geophone 175
7.12 MEMS-based Sensors 176
7.13 Shakers for Structure Excitation 177
7.14 Some Comments on Measurement Procedures 178
7.15 Problems 180
References 181
8 Frequency Analysis Theory 183
8.1 Periodic Signals - The Fourier Series 183
8.2 Spectra of Periodic Signals 185
8.3 Random Processes 187
8.4 Transient Signals 189
8.5 Interpretation of Spectra 189
8.6 Chapter Summary 191
8.7 Problems 192
References 193
9 Experimental Frequency Analysis 195
9.1 Frequency Analysis Principles 195
9.2 Octave and Third-Octave Band Spectra 197
9.3 The Discrete Fourier Transform (DFT) 198
9.4 Chapter Summary 224
9.5 Problems 225
References 226
10 Spectrum and Correlation Estimates Using the DFT 229
10.1 Averaging 229
10.2 Spectrum Estimators for Periodic Signals 230
10.3 Estimators for PSD and CSD 233
10.4 Estimators for Correlation Functions 250
10.5 Estimators for Transient Signals 258
10.6 A Signal Processing Framework for Spectrum and Correlation Estimation 260
10.7 Spectrum Estimation in Practice 262
10.8 Multichannel Spectral and Correlation Analysis 273
10.9 Chapter Summary 276
10.10 Problems 277
References 278
11 Measurement and Analysis Systems 281
11.1 Principal Design 282
11.2 Hardware for Noise and Vibration Analysis 283
11.3 FFT Analysis Software 295
11.4 Chapter Summary 299
11.5 Problems 300
Problems 300
References 301
12 Rotating Machinery Analysis 303
12.1 Vibrations in Rotating Machines 303
12.2 Understanding Time-Frequency Analysis 304
12.3 Rotational Speed Signals (Tachometer Signals) 306
12.4 RPM Maps 308
12.5 Smearing 310
12.6 Order Tracks 312
12.7 Synchronous Sampling 314
12.8 Averaging Rotation-Speed-Dependent Signals 317
12.9 Adding Change in RMS with Time 318
12.10 Parametric Methods 322
12.11 Chapter Summary 323
12.12 Problems 324
References 325
13 Single-input Frequency Response Measurements 327
13.1 Linear Systems 328
13.2 Determining Frequency Response Experimentally 328
13.3 Important Relationships for Linear Systems 333
13.4 The Coherence Function 333
13.5 Errors in Determining the Frequency Response 334
13.6 Coherent Output Power 339
13.7 The Coherence Function in Practice 340
13.8 Impact Excitation 342
13.9 Shaker Excitation 351
13.10 Examples of FRF Estimation - No Extraneous Noise 357
13.11 Example of FRF Estimation - With Output Noise 360
13.12 Examples of FRF Estimation - With Input and Output Noise 362
13.13 Chapter Summary 365
13.14 Problems 367
References 368
14 Multiple-Input Frequency Response Measurement 369
14.1 Multiple-Input Systems 369
14.2 Conditioned Input Signals 377
14.3 Bias and Random Errors for Multiple-Input Systems 384
14.4 Excitation Signals for MIMO Analysis 384
14.5 Data Synthesis and Simulation Examples 387
14.6 Real MIMO Data Case 393
14.7 Chapter Summary 396
14.8 Problems 397
References 398
15 Orthogonalization of Signals 401
15.1 Principal Components 401
15.2 Virtual Signals 410
15.3 Noise Source Identification (NSI) 417
15.4 Chapter Summary 422
15.5 Problems 423
References 424
16 Experimental Modal Analysis 425
16.1 Introduction to Experimental Modal Analysis 425
16.2 Experimental Setup 427
16.3 Introduction to Modal Parameter Extraction 437
16.4 SDOF Parameter Extraction 440
16.5 The Unified Matrix Polynomial Approach, UMPA 443
16.6 Time Versus Frequency Domain Parameter Extraction for EMA 452
16.7 Time Domain Parameter Extraction Methods 454
16.8 Frequency Domain Parameter Extraction Methods 470
16.9 Methods for Mode Shape Estimation and Scaling 480
16.10 Evaluating the Extracted Parameters 486
16.11 Chapter Summary 489
16.12 Problems 491
References 492
17 Operational Modal Analysis (OMA) 495
17.1 Principles for OMA 496
17.2 Data Acquisition Principles 497
17.3 OMA Modal Parameter Extraction for OMA 498
17.4 Scaling OMA Modal Models 508
17.5 Chapter Summary 512
17.6 Problems 514
References 514
18 Advanced Analysis Methods 517
18.1 Shock Response Spectrum 517
18.2 The Hilbert Transform 520
18.3 Cepstrum Analysis 527
18.4 The Envelope Spectrum 531
18.5 Creating Random Signals with Known Spectral Density 533
18.6 Identifying Harmonics in Noise 535
18.7 Harmonic Removal 539
18.8 Chapter Summary 542
18.9 Problems 543
References 544
19 Practical Vibration Measurements and Analysis 547
19.1 Introduction to a Plexiglas Plate 547
19.2 Forced Response Simulation 550
19.3 Spectra of Periodic Signals 556
19.4 Spectra of Random Signals 559
19.5 Data with Random and Periodic Content 561
19.6 Operational Deflection Shapes - ODS 567
19.7 Impact Excitation and FRF Estimation 572
19.8 Plexiglas EMA Example 578
19.9 Methods for EMA Modal Parameter Estimation, MPE 585
19.10 Conclusions of EMA MPE 599
19.11 OMA Examples 600
References 622
Appendix A Complex Numbers 625
Appendix B Logarithmic Diagrams 629
Appendix C Decibels 633
Appendix D Some Elementary Matrix Algebra 635
Appendix E Eigenvalues and the SVD 639
E.1 Eigenvalues and Complex Matrices 639
E.2 The Singular Value Decomposition (SVD) 640
Appendix F Organizations and Resources 643
Appendix G Checklist for Experimental Modal Analysis Testing 645
Bibliography 647
Index 659
