Topics in Modal Analysis & Testing, Volume 8 (eBook)

Preface 6
Contents 7
1 Modern Modal Testing: A Cautionary Tale 10
1.1 Introduction 10
1.2 Pitfall #1: Confusing Computer Jockeys and Engineers 11
1.3 Pitfall #2: Too Much Blind Faith in FEM's 11
1.4 Pitfall #3: Confusing Being Busy with Being Productive 12
1.5 Pitfall #4: Avoid Rushing to Analyze 12
1.6 Pitfall #5: Avoid Rushing to Test 13
1.7 Pitfall #6: Lack of Documentation 14
1.8 Pitfall #7: Designing Only for Design Loads 14
1.9 Pitfall #8: Modal Analysis Not Accounting for Out-of-Band Dynamics 15
1.10 Pitfall #9: Asking for Help or Seeking Advice Is a Sign of Weakness 15
1.11 Pitfall #10: Stove Piping: Separating Analysts and Test Engineers 15
1.12 Pitfall #11: Test Is a Four Letter Word 16
1.13 Pitfall #12: Unrealistic Success Criteria 16
1.14 Conclusion 17
References 17
2 Vibration Testing of Laparoscopic Surgical Instruments Under Varying Grip Pressures 18
2.1 Introduction 18
2.2 Background 19
2.3 Analysis 19
2.4 Conclusion 20
References 20
3 Combined Qualification Vibration Testing and Fixed Base Modal Testing Utilizing a Fixed Based Correction Method 21
3.1 Introduction 21
3.2 Simple Beam Pathfinder Study 22
3.3 Test Article Selection 23
3.4 FEM Construction and Sensor Pretest Trade Study 24
3.5 Bookend Free-Free Modal Test and Model Correlation 28
3.6 Multi-shaker Support Setup 31
3.7 Traditional Fixed Based Modal Test 32
3.8 Shaker Slip Table Modal Test 36
3.9 Future Work 37
3.10 Summary 38
References 38
4 Pressure Stiffened Modal Correlation of a Cylindrical Pressure Vessel 39
4.1 Introduction 39
4.2 Design of Pressure Vessel Using Finite Elements 40
4.2.1 Final Acoustoelastic Structure Design 40
4.2.2 Finite Element Results for Comparison 41
4.2.3 Required Pressure System Testing and Results 42
4.3 Modal Test of Acoustoelastic System 42
4.3.1 Modal Tap Test Results 43
4.4 Comparison of Experimentally Measured and Simulated Flex Modes 44
4.4.1 Predicted Versus Measured Shell Mode Frequencies 45
4.5 Conclusion 45
References 46
5 Pretest Analysis for Modal Survey Tests Using Fixed Base Correction Method 47
Nomenclature 47
5.1 Introduction 47
5.2 Motivation and Example Structure 48
5.3 Constraint Shape Calculation 50
5.4 Application of Constraint Shape to Frequency Response Function Calculation 52
5.5 Multipoint Constraint Method 54
5.6 Multipoint Constraint Fixed Base Correction Results 55
5.7 Formalized Procedure 59
5.8 Summary 60
References 60
6 Fixing Degrees of Freedom of an Aluminum Beam by Using Accelerometers as References 61
6.1 Introduction 61
6.2 Theoretical Background 61
6.3 Test Setup 62
6.4 Signal Processing 62
6.5 Test Results 64
6.6 Acceleration as References 65
6.7 Reaction Forces 65
6.8 Damping Discussion 66
6.9 Comparison to Analysis Model 67
6.10 Summary 68
References 68
7 Signal Reconstruction from Mobile Sensors Network Using Matrix Completion Approach 69
7.1 Introduction 69
7.2 Matrix Completion 72
7.3 Motivations 73
7.4 Problem Statement 73
7.5 Numerical Modeling 74
7.6 Comparing Methods 74
7.7 Conclusion 82
References 82
8 All Vibration Is a Summation of Mode Shapes 84
8.1 Introduction 85
8.1.1 Modal Testing 85
8.1.2 Curve Fitting 85
8.2 Expanding Experimental Data 85
8.3 Expanding Order-Based ODS's 86
8.4 Expanding Sinusoidal Responses 89
8.4.1 Response to In-Phase Forces 91
8.5 Modal Participation in Responses to In-Phase Forces 94
8.5.1 Response to Out-of-Phase Forces 95
8.5.2 Modal Participation in Responses to Out-of-Phase Forces 95
8.6 Conclusions 96
References 98
9 Modal Testing Using the Slinky Method 99
9.1 Introduction 99
9.1.1 Cross-channel Measurements 100
9.2 Transmissibility Properties 100
9.3 Slinky TRN Chain Measurement 100
9.4 Benefits of a TRN Chain 102
9.5 Seeding a TRN Chain 102
9.6 Round Trip Simulations 103
9.6.1 Experimental FRFs 104
9.7 MIMO Modeling and Simulation 105
9.8 Slinky Test of the Aluminum Plate 105
9.8.1 Seeding the TRN Chain with an FRF 106
9.8.2 Comparing Experimental and Slinky FRFs of the Plate 108
9.9 Slinky Test of Jim Beam 108
9.9.1 Seeding the TRN Chain with an FRF 108
9.9.2 Comparing Experimental and Slinky FRFs of the Jim Beam 109
9.10 Conclusion 110
References 111
10 Numerical and Experimental Modal Analysis of a Cantilever Beam Axially Loaded by a Tendon Which Is Attached in a Single Spanwise Location 112
10.1 Introduction 112
10.2 Theoretical Model 113
10.3 Numerical and Experimental Results 114
10.3.1 System with the Attachment Point in 0.5L 115
10.3.2 System with the Attachment Point in 0.9L 117
10.3.3 Stability of the System with One Attachment Point 118
10.4 Discussion 120
10.5 Conclusion 120
References 120
11 Designing a Modal Test Plan Based on Finite Element Method Results 122
11.1 Introduction 122
11.2 Simplifying Grids 122
11.3 Exciting Points Selection 125
11.4 Pure Normal Test 126
11.5 Conclusion 126
References 127
12 Maximizing the Quality of Shape Extractions from Base Shake Modal Tests 128
12.1 Introduction 128
12.2 Pretest Analysis 128
12.3 Accelerometer Selection 129
12.4 Exciter Selection 129
12.5 Test Conduct 130
12.6 Test Duration 130
12.7 Signal Processing 130
12.8 Mode Shape Calculation 130
12.9 Summary 131
References 131
13 New Approaches to Inverse Structural Modification Theory Using Random Projections 132
13.1 Introduction 132
13.2 Background and Methodology 134
13.2.1 The Generalised Eigenvalue Problem 134
13.2.2 Particle Swarm Optimisation 136
13.2.3 Random Embedding 137
13.3 Results 138
13.3.1 Ten-Dimensional Toy Problem 138
13.3.2 One-Dimensional Boeing-737 Finite Element Problem 140
13.4 Conclusion 144
Appendix: Boeing 737-300 Data and Formulation 145
References 147
14 Modal Analysis of Wind Turbine Blades with Different Test Setup Configurations 148
14.1 Introduction 148
14.2 Test Setups 149
14.3 Hammer vs. Shaker FRF Testing in Free-Free Boundary Conditions 150
14.4 Correlation with FE Model 151
14.5 Strain-Based Operational Modal Analysis 153
14.6 Pull-Release Test Results 155
14.7 Conclusions 156
References 157
15 Modal Excitation of Circular Rotating Structures Using an Innovative Electromagnetic Device 158
Nomenclature 158
15.1 Introduction 158
15.1.1 Dynamics of Cyclic Symmetric Structures 159
15.1.2 Electromagnetic Excitation 160
15.2 The Electromagnetic Excitation Device 161
15.2.1 Electromagnetic Force 161
15.2.2 Design 163
15.3 Experimental Results 164
15.4 Conclusions 166
References 166
16 Modal Analysis of a 7 DoF Sweet Pepper Harvesting Robot 168
16.1 Introduction 168
16.2 Experimental Setup 169
16.3 Preliminary Tests 170
16.3.1 Hammer Tip, Time Window and Bandwidth 170
16.3.2 Repeatability and Temperature Influence 171
16.3.3 Non-linearities and Influence of the Joint Controller 171
16.3.4 Influence of the Pose on the TCP Dynamics 172
16.4 Experimental Modal Analysis 173
16.5 Conclusions 174
References 175
17 Characterizing Dynamics of Additively Manufactured Parts 176
17.1 Introduction 176
17.1.1 Additive Manufacturing Background 177
17.1.1.1 Types of Additive Manufacturing 177
17.1.1.2 Opportunities of Additive Manufacturing 177
17.1.1.3 Defining and Refining Additive Manufacturing Material Performance 177
17.1.2 Digital Image Correlation Background 178
17.1.3 Objectives 178
17.2 Methodology 178
17.2.1 Design of Test Specimens 178
17.2.2 Digital Image Correlation Experimental Setup 180
17.3 Finite Element Model 181
17.4 Results and Discussion 183
17.4.1 Modal Analysis 183
17.4.2 Simulations 185
17.4.3 Discussion 186
17.5 Future Work 187
References 187
18 How Linear Is a Linear System? 189
18.1 Introduction 189
18.2 Subcomponent Definitions 190
18.3 Theory 191
18.3.1 Transmission Simulator Method 191
18.3.2 The Hilbert Transform 192
18.4 Linear Substructuring Tests and Predictions 193
18.4.1 Original Measurements 193
18.4.2 Example Hilbert Transform Analysis 194
18.4.3 Revised Measurements 194
18.5 Conclusions and Remarks 195
References 196
19 An Interpolation Algorithm to Speed Up Nonlinear Modal Testing Using Force Appropriation 197
19.1 Single Nonlinear Resonant Mode Method 197
19.2 Nonlinear FRF Interpolation Algorithm Overview 198
19.3 Case Study 199
19.4 Conclusion and Future Work 200
References 200
20 Estimating Applied Loads and Response Accelerations on a Dynamic System Using Vibration Data 201
20.1 Introduction 201
20.2 State Space Modeling of Vibratory Systems 202
20.3 Force Estimation Using Kalman Filter 203
20.4 Accelerometer Response Estimation Using Transfer Function of System 204
20.5 Analysis 205
20.6 Experimental Modal Analysis (EMA) 205
20.7 Comparison and Validation of the FE Model 207
20.8 Time Domain, Step Input Free Vibration Test of the GARTEUR Structure 208
20.9 Specifying Force Input Location by Using Augmented Kalman Filter 208
20.10 Mode-Based Steady-State Dynamics (SSD) Analysis 209
20.11 Frequency Domain Accelerometer Response Estimation Method 209
20.12 Conclusion 211
References 212
21 Analysis of Coupling Relationship Between Car-Body and Flexible Hanging Equipment 213
21.1 Introduction 213
21.2 Analysis Model of Equipment and Car-BODY 213
21.3 Excitation and Measure Points 214
21.3.1 Excitation of the Test 214
21.3.2 Measure Points 214
21.4 Test Analysis 215
21.4.1 Modal Parameters Identification 215
21.4.2 Vibration Transfer Characteristics 216
21.5 Conclusion 217
References 217
22 Imager-Based Characterization of Viscoelastic Material Properties 218
22.1 Introduction 218
22.2 Methodology 219
22.2.1 Modeling PBX in Intermediate Strain Rate 220
22.2.2 Imager-Based Modal Analysis Method 220
22.3 Experimental Setup 221
22.3.1 Challenges Addressed in the Experimental Setup 222
22.3.1.1 Excitation 223
22.3.1.2 Imaging 223
22.3.1.3 Illumination 223
22.4 Analysis 223
22.5 Conclusion 226
References 226
23 Development and Validation of Data Processing Techniques for Aircraft Ground Vibration Testing 228
23.1 Introduction 228
23.2 Conventional FRFs Computation 229
23.3 Virtual Driving Point Method for a Two Points Excitation Configuration 230
23.3.1 Adopted Procedure for the VDP Method Application 230
23.4 Validation Cases 232
23.4.1 Three DOFs Discrete System 232
23.4.2 Airplane Mockup: Polymax Stabilization Diagrams and Mode Shapes 233
23.4.3 Garteur Airplane Model: VDP Method Application to Data Measured During a Sine Sweep Test with a 90 Relative Phase Between Inputs 235
23.4.4 eFusion Magnus Aircraft: Non-linearities 237
23.5 Conclusions 239
References 239
24 Structural Health Monitoring with Self-Organizing Maps and Artificial Neural Networks 240
Notations 240
24.1 Introduction 241
24.2 The Damage Detection Algorithm 241
24.2.1 SOM Training 241
24.2.2 Structural Damage Assessment 242
24.3 The Grid Structure 242
24.4 Damage Scenario 1: 50% Local Stiffness Reduction on Cross Beams 243
24.5 Damage Scenario 2: Rigidity Changes in Boundary Conditions 243
24.5.1 Introducing a Pattern Recognition Neural Network 245
24.6 Conclusions 247
References 249
25 A Novel Technique to Extract the Modal Damping Properties of a Thin Blade 250
25.1 Introduction 250
25.2 A Novel Method to Extract Damping 251
25.3 Results 251
25.4 Conclusion 252
References 253
26 Finite Element Model Updating of the UCF Grid Benchmark Connections Using ExperimentalModal Data 254
26.1 Introduction 254
26.2 Model Updating 255
26.3 Modal Extraction and System Identification 256
26.4 UCF Grid and Impact Test 256
26.5 Finite Element Modeling of the UCF Grid 257
26.6 Parameter Estimation Analysis 259
26.6.1 One-Parameter Estimation Analysis 260
26.6.2 Two-Parameter Estimation Analysis 261
26.7 Conclusion 263
References 264
27 Structural Health Monitoring on Industrial Structures Using a Combined Numerical and Experimental Approach 265
27.1 Historical Introduction 265
27.2 Introduction to the Project 266
27.3 Materials and Methods 267
27.4 Test Results and Discussion 268
27.5 Model Correlation and Fe Model Updating 269
27.6 Damages Sensitivity Study 271
27.7 Conclusion 276
27.8 Further Work 277
References 279
28 Validation of Automatic Modal Parameter Estimator on a Car Body-in-White 280
28.1 Introduction 280
28.2 Theoretical Background 281
28.3 Methodology 282
28.4 Results 282
28.5 Conclusions 284
References 285
29 Modal Analysis of Rotating Tires in Stationary and Rotating Frames of Reference 286
29.1 Introduction 286
29.2 Experimental Setup 287
29.2.1 Stationary Frame-of-Reference Experimental Setup 287
29.2.2 Rotating Frame-of-Reference Experimental Setup 288
29.3 Results and Discussion 288
29.3.1 Rotating Frame-of-Reference 288
29.3.2 Stationary Frame-of-Reference 289
29.4 Conclusions 291
References 291
30 Combining Machine Learning and Operational Modal Analysis Approaches to Gain Insights in Wind Turbine Drivetrain Dynamics 293
30.1 Introduction 293
30.2 Theoretical Background 294
30.3 Methodology 296
30.3.1 Use of Big Data Analysis and Tailored Database 296
30.3.2 Signal Classification 296
30.3.3 Automation of Modal Analysis for Rotating Machines 297
30.4 Results 297
30.5 Conclusions 299
References 299
31 Modal Test-Analysis Correlation Using Left-Hand Eigenvectors 300
31.1 Introduction 300
31.2 Nomenclature 301
31.3 Test Mode Orthogonality and Test-Analysis Correlation 301
31.3.1 Modal Test-Analysis Correlation (Established U.S. Government Standards) 301
31.3.2 Modal Test Data Resulting from Estimated State-Space Models 302
31.3.3 Theoretical System Modes in State-Space Form 303
31.3.4 Correlation of Experimental and Theoretical Modes (Left-Hand Eigenvectors) 304
31.3.5 Correlation of Experimental and Theoretical Modes (Complex Least Squares) 304
31.4 ISPE Test-TAM Correlation 305
31.4.1 Orthogonality and Test-TAM Correlation (Using Left-Hand Eigenvectors) 306
31.4.2 Orthogonality and Test-TAM Correlation (Using Complex Least Squares) 306
31.5 Complex Least-Squares Test-TAM Correlation Study Based on Simulations 307
31.6 Conclusions 309
References 309
32 A Theoretical Study on the Generation and Propagation of Traveling Waves in Strings 310
32.1 Introduction 310
32.2 Analysis of the One-Dimensional Equation of Motion for Strings 310
32.3 Conclusion 314
References 314
33 Shaping the Frequency Response Function (FRF) of a Multi-Degree-of-Freedom (MDOF) Structure Using Arrays of Tuned Vibration Absorbers (TVA) 316
33.1 Introduction 316
33.2 Experiment Setup and Testing Procedure 317
33.3 Modeling 318
33.4 Results and Discussion 320
33.4.1 Experimental Results 320
33.4.2 Lumped-Parameter Model Results 322
33.4.3 Comparing Experimental and Modeling Results 322
33.5 Conclusion 324
References 325
34 Experimental Study on Tire Vibrations and Induced Noise 326
34.1 Introduction 326
34.2 Test Set-Up 327
34.3 Measurement Results 328
34.4 Conclusions 330
References 331
35 On the Adaptive Vibration Suppression on a Flexible Spatial Structure 332
35.1 Introduction 332
35.2 Description and Modal Model of the System 333
35.3 On-Line Algebraic Modal Parameter Identification Approach 335
35.4 Adaptive-Like Multi Positive Position Feedback Control Scheme 335
35.5 Experimental Setup and Results 336
35.6 Conclusions 338
References 338
36 Evaluation of the Human-Structure-Soil Interaction on a Two-Wheel Tractor Using Modal Analysis Techniques 339
36.1 Introduction 339
36.2 Background 339
36.3 Modal Analysis of a Two-Wheel Tractor Handlebar 340
36.4 Experimental Modal Analysis of a Handlebar 342
36.5 Operational Modal Analysis 343
36.6 Discussion 345
36.7 Conclusion 346
References 346
37 Reproducible Modal Testing Using a Flexure-Based Impact Excitation System 347
37.1 Brief Introduction 347
37.2 Impact Excitation System 348
37.3 Preliminary Results 348
37.4 Conclusions 350
References 350
38 Modal Analysis and Characterization of Mounting Cart Used for Testing in the Combined Environment Acoustic Chamber 351
38.1 Introduction 351
38.2 Background 351
38.3 Analysis 352
38.4 Conclusion 353
Reference 353
39 Effects of Sensor Count on Damping Estimates from Operational Modal Analysis 354
39.1 Introduction 354
39.2 Method 355
39.3 Setup and Analysis 355
39.4 Results 356
39.5 Reference Based Estimation: The Size of the Hankel Matrix 357
39.6 Discussion and Conclusions 361
References 361
40 Ambient Vibration Tests and Modal Response Analysis of an Old Age High-Rise Building in Downtown Vancouver, Canada 362
40.1 Introduction 362
40.2 Building Description and Test Plan 362
40.3 Modal Analysis 363
40.4 Results and Conclusion 363
References 364
41 System Identification of a Full Scale Wood Frame Building Specimen Subjected to Shake Table Tests 366
41.1 Introduction 366
41.2 Building Description and Shake Table Tests 366
41.3 Modal Analysis 367
41.4 Results and Conclusion 368
References 368
42 Estimating Rotor Suspension Parameters from Runout Data 369
42.1 Introduction 369
42.2 Method for Estimating Rotor Suspension Dynamic Characteristics from Runout Data 369
42.3 Estimating the Dynamic Characteristics of a Rotor Suspension 371
42.4 Conclusion 376