Modal Testing - Avitabile Peter | Libro Wiley–Blackwell 11/2017 - HOEPLI.it


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Modal Testing

A Practitioner's Guide




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Genere:Libro
Lingua: Inglese
Pubblicazione: 11/2017





Note Editore

The practical, clear, and concise guide for conducting experimental modal tests

Modal Testing: A Practitioner's Guide outlines the basic information necessary to conduct an experimental modal test. The text draws on the author's extensive experience to cover the practical side of the concerns that may arise when performing an experimental modal test. Taking a hands–on approach, the book explores the issues related to conducting a test from start to finish. It covers the cornerstones of the basic information needed and summarizes all the pertinent theory related to experimental modal testing.

Designed to be accessible, Modal Testing presents the most common excitation techniques used for modal testing today and is filled with illustrative examples related to impact testing which is the most widely used excitation technique for traditional experimental modal tests. This practical text is not about developing the details of the theory but rather applying the theory to solve real–life problems, and:

  • Delivers easy to understand explanations of complicated theoretical concepts
  • Presents basic steps of an experimental modal test
  • Offers simple explanations of methods to obtain good measurements and avoid the common blunders typically found in many test approaches
  • Focuses on the issues to be faced when performing an experimental modal test
  • Contains full–color format that enhances the clarity of the figures and presentations

Modal Testing: A Practitioner's Guide is a groundbreaking reference that treats modal testing at the level of the practicing engineer or a new entrant to the field of experimental dynamic testing.





Sommario

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

3.15 Input Output Model with Noise 127

3.15.1 H1 Formulation: Output Noise Only 127

3.15.2 H2 Formulation: Output Noise Only 128

3.15.3 H1 Formulation: Input Noise Only 128

3.15.4 H2 Formulation: Input Noise Only 128

3.16 Summary 129

4 Excitation Techniques 131

4.1 Introduction 131

4.2 Impact Excitation Technique 132

4.2.1 Impact Hammer 132

4.2.2 Hammer Impact Tip Selection 136

4.2.3 Useful Frequency Range for Impact Excitation 137

4.2.4 ForceWindow for Impact Excitation 137

4.2.5 Pre–trigger Delay 137

4.2.6 Double Impact 140

4.2.7 Response due to Impact 140

4.2.8 Roving Hammer vs Stationary Hammer and Reciprocity 143

4.2.9 Impact Testing: an Example Set of Measurements 147

4.3 Shaker Excitation 159

4.3.1 Modal Shaker Setup 161

4.3.2 Historical Development of Shaker Excitation Techniques 162

4.3.3 Swept Sine Excitation 163

4.3.4 Pure Random Excitation 163

4.3.5 Pure Random Excitation withWindows Applied 165

4.3.6 Pure Random Excitation with Overlap Processing 165

4.3.7 Pseudo–random Excitation 167

4.3.8 Periodic Random Excitation 167

4.3.9 Burst Random Excitation 168

4.3.10 Sine Chirp Excitation 170

4.3.11 Digital Stepped Sine Excitation 170

4.4 Comparison of Different Excitations for aWeldment Structure 172

4.4.1 Random Excitation with NoWindow 172

4.4.2 Random Excitation with HanningWindow 173

4.4.3 Burst Random Excitation with NoWindow 173

4.4.4 Sine Chirp Excitation with NoWindow 174

4.4.5 Comparison of Random, Burst Random and Sine Chirp 175

4.4.6 Comparison of Random and Burst Random at Resonant Peaks 175

4.4.7 Linearity Check Using Sine Chirp 175

4.5 Multiple–input,Multiple–outputMeasurement 175

4.5.1 Multiple Input vs Single Input Testing 177

4.5.2 Multiple Input vs Single Input for aWeldment Structure 181

4.5.3 Multiple Input vs Single Input Testing 181

4.5.4 Comparison of Multiple Input and Single Input forWeldment Structure 182

4.5.5 MIMO Measurements on a Multi–component Structure 182

4.6 Summary 187

5 Modal Parameter Estimation Techniques 189

5.1 Introduction 189

5.2 ExperimentalModal Analysis 190

5.2.1 Least Squares Approximation of Data 190

5.2.2 Classification of Modal Parameter Estimation Techniques 193

5.3 Extraction of Modal Parameters 198

5.3.1 Peak Picking Technique 198

5.3.2 Circle Fitting Kennedy and Pancu 199

5.3.3 SDOF Polynomial 200

5.3.4 Residual Effects of Out of Band Modes 200

5.3.5 MDOF Polynomial 201

5.3.6 Least Squares Complex Exponential 201

5.3.7 Advanced Forms of Time and Frequency Domain Estimators 203

5.3.8 General Time Domain Techniques 203

5.3.9 General Frequency Domain Techniques 203

5.3.10 General Consideration for Time vs Frequency Representation 204

5.3.11 Additional Remarks on Modal Parameter Estimation 204

5.3.12 Two Step Process for Modal Parameter Estimation 205

5.4 Mode Identification Tools 206

5.4.1 Summation Function 206

5.4.2 Mode Indicator Function 206

5.4.3 Complex Mode Indicator Function 207

5.4.4 Stability Diagram 208

5.4.5 PolyMAX 210

5.5 Modal Model Validation Tools 212

5.5.1 Synt





Autore

PETER AVITABILE is Professor Emeritus at the University of Massachusetts Lowell, the co–director of the Structural Dynamics and Acoustic Systems Laboratory, and the former President for the Society for Experimental Mechanics. In addition, he is the Associate Editor of the Handbook for Experimental Structural Mechanics. He has written hundreds of papers and articles on analytical and experimental modal analysis techniques, including the Modal Space article series published in SEM's Experimental Techniques.








Altre Informazioni

ISBN: 9781119222897
Condizione: Nuovo
Dimensioni: 259 x 29.77 x 180 mm Ø 1304 gr
Formato: Copertina rigida
Pagine Arabe: 544






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