Anders Brandt is a Professor and Head of the Department of Mechanical and Production Engineering at Aarhus University in Denmark. His research interests include vibration analysis, experimental and operational modal analysis, signal analysis, and system identification. He worked for 20 years in industry in Sweden and abroad, and gave over 250 short-courses on various topics in the field of vibration engineering. He is a member of the Society for Experimental Mechanics and is on the scientific committee for the International Operational Modal Analysis Conference.

• About the Author xixPreface xxiAcknowledgments xxvList of Abbreviations xxviiAnnotation xxix1 Introduction 11.1 Noise and Vibration 11.2 Noise and Vibration Analysis 21.3 Application Areas 31.4 Analysis of Noise and Vibrations 41.5 Standards 51.6 Becoming a Noise and Vibration Analysis Expert 52 Dynamic Signals and Systems 92.1 Introduction 92.2 Periodic Signals 112.3 Random Signals 162.4 Transient Signals 172.5 RMS Value and Power 182.6 Linear Systems 192.7 The Continuous Fourier Transform 292.8 Chapter Summary 352.9 Problems 36References 383 Time Data Analysis 393.1 Introduction to Discrete Signals 393.2 The Sampling Theorem 403.3 Filters 483.4 Time Series Analysis 573.5 Chapter Summary 663.6 Problems 67References 684 Statistics and Random Processes 714.1 Introduction to the Use of Statistics 714.2 Random Theory 734.3 Statistical Methods 834.4 Quality Assessment of Measured Signals 914.5 Chapter Summary 944.6 Problems 95References 965 Fundamental Mechanics 975.1 Newton’s Laws 975.2 The Single Degree-of-Freedom System (SDOF) 985.3 Alternative Quantities for Describing Motion 1065.4 Frequency Response Plot Formats 1085.5 Determining Natural Frequency and Damping Ratio 1135.6 Rotating Mass 1155.7 Some Comments on Damping 1165.8 Models Based on SDOF Approximations 1185.9 The Two Degree of Freedom System (2DOF) 1215.10 The Tuned Damper 1235.11 Chapter Summary 1255.12 Problems 126References 1276 Modal Analysis Theory 1296.1 Waves on a String 1296.2 Matrix Formulations 1316.3 Eigenvalues and Eigenvectors 1326.4 Frequency Response of MDOF Systems 1466.5 Free Decays 1556.6 Chapter Summary 1566.7 Problems 157References 1587 Transducers for Noise and Vibration Analysis 1597.1 The Piezoelectric Effect 1597.2 The Charge Amplifier 1607.3 Transducers with Built-In Impedance Converters, “IEPE” 1627.4 The Piezoelectric Accelerometer 1657.5 The Piezoelectric Force Transducer 1707.6 The Impedance Head 1717.7 The Impulse Hammer 1727.8 Accelerometer Calibration 1737.9 Measurement Microphones 1747.10 Microphone Calibration 1757.11 The Geophone 1757.12 MEMS-based Sensors 1767.13 Shakers for Structure Excitation 1777.14 Some Comments on Measurement Procedures 1787.15 Problems 180References 1818 Frequency Analysis Theory 1838.1 Periodic Signals – The Fourier Series 1838.2 Spectra of Periodic Signals 1858.3 Random Processes 1878.4 Transient Signals 1898.5 Interpretation of Spectra 1898.6 Chapter Summary 1918.7 Problems 192References 1939 Experimental Frequency Analysis 1959.1 Frequency Analysis Principles 1959.2 Octave and Third-Octave Band Spectra 1979.3 The Discrete Fourier Transform (DFT) 1989.4 Chapter Summary 2249.5 Problems 225References 22610 Spectrum and Correlation Estimates Using the DFT 22910.1 Averaging 22910.2 Spectrum Estimators for Periodic Signals 23010.3 Estimators for PSD and CSD 23310.4 Estimators for Correlation Functions 25010.5 Estimators for Transient Signals 25810.6 A Signal Processing Framework for Spectrum and Correlation Estimation 26010.7 Spectrum Estimation in Practice 26210.8 Multichannel Spectral and Correlation Analysis 27310.9 Chapter Summary 27610.10 Problems 277References 27811 Measurement and Analysis Systems 28111.1 Principal Design 28211.2 Hardware for Noise and Vibration Analysis 28311.3 FFT Analysis Software 29511.4 Chapter Summary 29911.5 Problems 300Problems 300References 30112 Rotating Machinery Analysis 30312.1 Vibrations in Rotating Machines 30312.2 Understanding Time–Frequency Analysis 30412.3 Rotational Speed Signals (Tachometer Signals) 30612.4 RPM Maps 30812.5 Smearing 31012.6 Order Tracks 31212.7 Synchronous Sampling 31412.8 Averaging Rotation-Speed-Dependent Signals 31712.9 Adding Change in RMS with Time 31812.10 Parametric Methods 32212.11 Chapter Summary 32312.12 Problems 324References 32513 Single-input Frequency Response Measurements 32713.1 Linear Systems 32813.2 Determining Frequency Response Experimentally 32813.3 Important Relationships for Linear Systems 33313.4 The Coherence Function 33313.5 Errors in Determining the Frequency Response 33413.6 Coherent Output Power 33913.7 The Coherence Function in Practice 34013.8 Impact Excitation 34213.9 Shaker Excitation 35113.10 Examples of FRF Estimation – No Extraneous Noise 35713.11 Example of FRF Estimation – With Output Noise 36013.12 Examples of FRF Estimation – With Input and Output Noise 36213.13 Chapter Summary 36513.14 Problems 367References 36814 Multiple-Input Frequency Response Measurement 36914.1 Multiple-Input Systems 36914.2 Conditioned Input Signals 37714.3 Bias and Random Errors for Multiple-Input Systems 38414.4 Excitation Signals for MIMO Analysis 38414.5 Data Synthesis and Simulation Examples 38714.6 Real MIMO Data Case 39314.7 Chapter Summary 39614.8 Problems 397References 39815 Orthogonalization of Signals 40115.1 Principal Components 40115.2 Virtual Signals 41015.3 Noise Source Identification (NSI) 41715.4 Chapter Summary 42215.5 Problems 423References 42416 Experimental Modal Analysis 42516.1 Introduction to Experimental Modal Analysis 42516.2 Experimental Setup 42716.3 Introduction to Modal Parameter Extraction 43716.4 SDOF Parameter Extraction 44016.5 The Unified Matrix Polynomial Approach, UMPA 44316.6 Time Versus Frequency Domain Parameter Extraction for EMA 45216.7 Time Domain Parameter Extraction Methods 45416.8 Frequency Domain Parameter Extraction Methods 47016.9 Methods for Mode Shape Estimation and Scaling 48016.10 Evaluating the Extracted Parameters 48616.11 Chapter Summary 48916.12 Problems 491References 49217 Operational Modal Analysis (OMA) 49517.1 Principles for OMA 49617.2 Data Acquisition Principles 49717.3 OMA Modal Parameter Extraction for OMA 49817.4 Scaling OMA Modal Models 50817.5 Chapter Summary 51217.6 Problems 514References 51418 Advanced Analysis Methods 51718.1 Shock Response Spectrum 51718.2 The Hilbert Transform 52018.3 Cepstrum Analysis 52718.4 The Envelope Spectrum 53118.5 Creating Random Signals with Known Spectral Density 53318.6 Identifying Harmonics in Noise 53518.7 Harmonic Removal 53918.8 Chapter Summary 54218.9 Problems 543References 54419 Practical Vibration Measurements and Analysis 54719.1 Introduction to a Plexiglas Plate 54719.2 Forced Response Simulation 55019.3 Spectra of Periodic Signals 55619.4 Spectra of Random Signals 55919.5 Data with Random and Periodic Content 56119.6 Operational Deflection Shapes – ODS 56719.7 Impact Excitation and FRF Estimation 57219.8 Plexiglas EMA Example 57819.9 Methods for EMA Modal Parameter Estimation, MPE 58519.10 Conclusions of EMA MPE 59919.11 OMA Examples 600References 622Appendix A Complex Numbers 625Appendix B Logarithmic Diagrams 629Appendix C Decibels 633Appendix D Some Elementary Matrix Algebra 635Appendix E Eigenvalues and the SVD 639E.1 Eigenvalues and Complex Matrices 639E.2 The Singular Value Decomposition (SVD) 640Appendix F Organizations and Resources 643Appendix G Checklist for Experimental Modal Analysis Testing 645Bibliography 647Index 659