Topics in Modal Analysis & Testing, Volume 8

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

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