Modal Testing: A Practitioner's Guide (Hardcover)

Preface xv About the CompanionWebsite xix Part I Overview of Experimental Modal Analysis using the Frequency Response Method 1 1 Introduction to ExperimentalModal Analysis: A Simple Non-mathematical Presentation 3 1.1 Could you Explain Modal Analysis to Me? 6 1.2 Just what are these Measurements called FRFs? 10 1.2.1 Why is Only One Row or Column of the FRF Matrix Needed? 13 1.3 What's the Difference between a Shaker Test and an Impact Test? 17 1.3.1 What Measurements do we Actually make to Compute the FRF? 18 1.4 What's the Most ImportantThing toThink about when Impact Testing? 21 1.5 What's the Most ImportantThing toThink about when Shaker Testing? 22 1.6 Tell me More AboutWindows; They Seem Pretty Important! 24 1.7 So how do we get Mode Shapes from the Plate FRFs? 25 1.8 Modal Data and Operating Data 29 1.8.1 What is Operating Data? 29 1.8.2 So what Good is Modal Data? 33 1.8.3 So Should I Collect Modal Data or Operating Data? 34 1.9 Closing Remarks 36 2 General Theory of Experimental Modal Analysis 37 2.1 Introduction 37 2.2 Basic Modal AnalysisTheory - SDOF 38 2.2.1 Single Degree of Freedom System Equation 38 2.2.2 Single Degree of Freedom System Response due to Harmonic Excitation 40 2.2.3 Damping Estimation for Single Degree of Freedom System 42 2.2.4 Response Assessment with Varying Damping 43 2.2.5 Laplace Domain Approach for Single Degree of Freedom System 46 2.2.6 System Transfer Function 47 2.2.7 Different Forms of the Transfer Function 48 2.2.8 Residue of the SDOF System 49 2.2.9 Frequency Response Function for a Single Degree of Freedom System 49 2.2.10 Transfer Function/Frequency Response Function/S-plane for a Single Degree of Freedom System 51 2.2.11 Frequency Response Function Regions for a Single Degree of Freedom System 51 2.2.12 Different Forms of the Frequency Response Function 53 2.2.13 Complex Frequency Response Function 53 2.3 Basic Modal AnalysisTheory - MDOF 56 2.3.1 Multiple Degree of Freedom System Equations 57 2.3.2 Laplace Domain for Multiple Degree of Freedom System 66 2.3.3 The Frequency Response Function 68 2.3.4 Mode Shapes from Frequency Response Equations 68 2.3.5 Point-to-Point Frequency Response Function 71 2.3.6 Response of Multiple Degree of Freedom System to Harmonic Excitations 72 2.3.7 Example: Cantilever Beam Model with Three Measured DOFs 75 2.3.8 Summary of Time, Frequency, and Modal Domains 83 2.3.9 Response due to Forced Excitation using Mode Superposition 87 2.4 Summary 89 3 General Signal Processing andMeasurements Related to Experimental Modal Analysis 93 3.1 Introduction 93 3.2 Time and Frequency Domain 93 3.3 Some General Information Regarding Data Acquisition 96 3.4 Digitization of Time Signals 97 3.5 Quantization 97 3.5.1 ADC Underload 98 3.5.2 ADC Overload 100 3.6 AC Coupling 100 3.7 SamplingTheory 101 3.8 Aliasing 103 3.9 What is the Fourier Transform? 105 3.9.1 Fourier Transform and Discrete Fourier Transform 107 3.9.2 FFT: Periodic Signal 108 3.9.3 FFT: Non-periodic Signal 108 3.10 Leakage and Minimization of Leakage 109 3.10.1 Minimization of Leakage 111 3.11 Windows and Leakage 111 3.11.1 RectangularWindow 112 3.11.2 HanningWindow 116 3.11.3 Flat TopWindow 116 3.11.4 Comparison ofWindows withWorst Leakage Distortion Possible 116 3.11.5 Comparison of Rectangular, Hanning and Flat TopWindow 119 3.11.6 ForceWindow 119 3.11.7 ExponentialWindow 119 3.11.8 Convolution of theWindow in the Frequency Domain 119 3.12 Frequency Response Function Formulation 119 3.13 TypicalMeasurements 123 3.13.1 Time Signal and Auto-power Functions 123 3.13.2 TypicalMeasurement: Cross Power Function 124 3.13.3 TypicalMeasurement: Frequency Response Function 124 3.13.4 TypicalMeasurement: Coherence Function 124 3.14 Time and Frequency Relationship Definition 126 3