Topics in Modal Analysis II, Volume 8

Preface	6
Contents	8
Chapter 1 Integrating Multiple Algorithms in Autonomous Modal Parameter Estimation	11
1.1 Introduction	12
1.2 Background	12
1.2.1 Spatial Information	12
1.2.2 Autonomous Modal Parameter Estimation	13
1.2.3 Pole Weighted Modal Vectors	13
1.3 Multi-algorithm, Extended Consistency Diagrams	15
1.4 Autonomous Modal Parameter Estimation with Extended Consistency Diagrams	17
1.5 Summary and Future Work	18
References	19
Chapter 2 Effects of Magneto-Mechanical Coupling on Structural Modal Parameters	20
2.1 Introduction	20
2.2 The Test Setup	21
2.2.1 Emerging Effects	21
2.2.2 Mathematical Description of the System	22
2.2.3 Parameter Identification	22
2.3 3D FEM Model	23
2.4 Measurements	26
2.5 Results	27
2.6 Conclusion and Outlook	27
References	27
Chapter 3 Extraction of Modal Parameters of Micromachined Resonators in Higher Modes	28
3.1 Introduction	28
3.2 Theory	29
3.2.1 Functional Description	29
3.2.2 Numerical Procedure	30
3.2.3 Experimental Procedure	30
3.3 Results and Discussion	30
3.3.1 Natural Frequency	31
3.3.2 Damping	34
3.3.3 Influence of Loading	35
3.4 Conclusion	36
References	36
Chapter 4 Normalization of Experimental Modal Vectors to Remove Modal Vector Contamination	37
4.1 Introduction	38
4.2 Background	38
4.2.1 Modal Vectors from Weighted Estimation of Residues	38
4.2.2 Modal Assurance Criterion	39
4.2.2.1 Special Forms of the Modal Assurance Criterion	40
4.2.3 Modal Vector Contamination: Simple Example	41
4.3 Normalization of the Modal Weighting (Participation) Vector	41
4.3.1 Central Axis Rotation	41
4.3.2 Modal Vector Complexity	42
4.3.3 Proposed New Methodology	43
4.4 15 DOF Analytical Example	43
4.5 C-Plate Example	43
4.5.1 C-Plate Example: Estimates with Complex Weighting	45
4.5.2 C-Plate Example: Estimates with Real Weighting	46
4.6 Summary and Future Work	48
References	49
Chapter 5 Effective Use of Scanning Laser Doppler Vibrometers for Modal Testing	50
5.1 Introduction	50
5.1.1 Scope of Paper	50
5.1.2 Introduction to SLDVs	50
5.2 Use of SLDVs in Modal Analysis	51
5.2.1 Changes to Test Design	51
5.2.2 Import of SLDV Data: The Universal File Format	53
5.2.2.1 Origin of the Universal File Format	53
5.2.2.2 Important UFF Datasets for Modal Analysis	53
5.2.2.3 UFF and SLDV	54
5.2.3 Management of Hybrid Datasets	54
5.2.4 Matching SLDV Test Geometries to FE Models	54
5.3 Case Study	56
5.3.1 Virtual Testing and Experimental Analysis	56
5.3.2 Experimental Modal Analysis and Model Correlation	59
5.3.3 Model Updating	60
5.3.3.1 Model Updating Using Global Parameters of Component Subsets	61
5.3.3.2 Model Updating Using Local Parameters	62
5.4 Conclusions	64
References	65
Chapter 6 Precise Frequency Domain Algorithm of Half Spectrum and FRF	66
6.1 Introduction	66
6.2 Precise Frequency Domain Algorithm	68
6.2.1 Half Spectrum	68
6.2.2 Impact Test	69
6.2.3 Continuous Exciting	70
6.3 Examples	70
6.3.1 Precise Half Spectrum and Coherence Function	70
6.3.2 Impact Test and Coherence Function	71
6.4 Conclusions	75
References	76
Chapter 7 Identification of a Time-Varying Beam Using Hilbert Vibration Decomposition	77
7.1 Introduction	77
7.2 The Hilbert-Huang Transform as a Tool to Compute Instantaneous Properties of Multi-Component Signals	77
7.2.1 The Empirical Mode Decomposition as Sifting Process	78
7.2.2 The Hilbert Transform and the Analytic Signal for the Extraction of Instantaneous Characteristics	78
7.3 The Hilbert Vibration Decomposition Method	79
7.4 Drawbacks of the HHT and HVD Methods	79
7.5 Modified Hilbert Vibration Decomposition Method	81
7.5.1 Addition of a Source Separation Step to Avoid Mode Switching	81
7.5.2 Instantaneous Phase/Frequency and Mode Deflection Shapes Calculation	82
7.6 Numerical Application	83
7.6.1 Identification of Instantaneous Frequencies	84
7.6.2 Component Extraction and Calculation of Mode Deflection Shapes	84
7.7 Conclusion	85
References	87
Chapter 8 Recovery of Operational Deflection Shapes from Noise-Corrupted Measurement Data from CSLDV: Comparison Between Polynomial and Mode Filtering Approaches	88
8.1 Introduction	88
8.2 Measurement of ODSs of LINX Tail Cone Using CSLDV	89
8.2.1 Step Scanning Method	89
8.2.2 Investigation of Stepped Scan and Continuous Scan Signals	90
8.2.3 Continuous Scanning LDV Method	91
8.2.4 Mode Matching Analysis	91
8.3 Conclusions	93
References	96
Chapter 9 Exploiting Imaging Techniques to Overcome the Limits of Vibration Testing in High Excitation Level Conditions	97
9.1 Introduction	97
9.2 Camera-Based and LDV-Based Tests Set-Up	98
9.3 Image Processing Method	99
9.4 Analysis of Results	100
9.4.1 Sensitivity to Spatial Resolution	100
9.4.2 Sensitivity to Spatial Averaging	100
9.4.3 Sensitivity to Edge Effects	100
9.5 Conclusion	103
References	104
Chapter 10 An Experimental Modal Channel Reduction Procedure Using a Pareto Chart	105
10.1 Introduction	105
10.2 Theory	106
10.3 Test Description	107
10.4 Results	108
10.5 Modal Testing	109
10.6 Finite Element Modeling	111
10.7 Conclusion	113
References	113
Chapter 11 Unique Isolation Systems to Protect Equipment in Navy Shock Tests	115
11.1 Introduction	115
11.2 Seamount Isolators	116
11.2.1 Description of the Isolator	117
11.3 Family of Seamounts	117
11.4 Barge Test Program	118
11.4.1 Dummy Loaded Isolated Racks	118
11.5 Test Series	119
11.5.1 Shock Severity: Acceleration and Pseudo Velocity (PV)	120
11.5.2 Analysis of Measured Data	121
11.6 Survey of Barge Test Shock Results: Acceleration—Time, SRS, Fourier Analysis	121
11.6.1 8 Hz Deck Measurements	121
11.6.2 Correlation of the Fourier Spectrum and SRS	123
11.6.3 14 Hz Deck Measurements	126
11.6.4 Barge Test of a Fully Populated Rack	129
11.7 Summary and Conclusions	130
References	131
Chapter 12 Nonlinear High Fidelity Modeling of Impact Load Response in a Rod	132
12.1 Introduction	132
12.2 Modeling	133
12.2.1 Nonlinear Rod Model	133
12.2.2 Alternating Wavelet-Time Finite Element Method	134
12.3 Experiments and Numerical Simulations	134
12.3.1 Experimental Setup	134
12.3.2 Numerical Simulations	136
12.4 Concluding Remarks	137
References	137
Chapter 13 On the Role of Boundary Conditions in the Nonlinear Dynamic Response of Simple Structures	138
13.1 Introduction	138
13.2 Modeling	139
13.2.1 Rod Model	139
13.2.2 Beam Model	140
13.2.3 Alternating Wavelet-Time Finite Element Method	141
13.3 Numerical Simulations	141
13.3.1 Rod	141
13.3.2 Beam	142
13.4 Concluding Remarks	145
References	146
Chapter 14 Evaluation of On-Line Algebraic Modal Parameter Identification Methods	147
14.1 Introduction	147
14.2 Vibrating Mechanical System	148
14.3 On-Line Algebraic Parameter Identification of Modal Parameters	149
14.4 An Illustrative Case: Simulation and Experimental Results	152
14.5 Conclusions	154
References	154
Chapter 15 Ambient Vibration Test of Granville Street Bridge Before Bearing Replacement	155
15.1 Introduction	155
15.2 Description of the Bridge	156
15.3 Description of the Ambient Vibration Test	157
15.4 Data Analysis	157
15.5 Analysis Results	158
15.6 Conclusion	159
Reference	161
Chapter 16 Vibration Testing and Analysis of A Monumental Stair	162
16.1 Introduction	162
16.2 Description of the Staircase	164
16.3 Description of the Dynamic Tests	164
16.4 Analytical Modeling of the Staircase	165
16.5 Comparison of the Estimated Analytical and Measured Dynamic Properties	165
16.6 Comparison of the Measured and Analytical Mode Shapes	166
16.7 Comparison of the Analytical and Measured Responses	168
16.8 Evaluating the Stair Vibrations	169
16.9 Conclusions	169
References	169
Chapter 17 Evaluation of Stop Bands in Periodic and Semi-Periodic Structures by Experimental and Numerical Approaches	171
17.1 Introduction	171
17.2 Stop-Bands in Periodic One-Dimensional Waveguides	172
17.2.1 Periodic One-Dimensional Waveguides	172
17.2.2 Semi-Periodic One-Dimensional Waveguide	173
17.3 Numerical Examples and Experimental Results	174
17.4 Conclusions	177
References	178
Chapter 18 Operating Mode Shapes of Electronic Assemblies Under Shock Input	179
18.1 Introduction	179
18.2 Test Setup	180
18.3 Finite Element Simulation	180
18.3.1 Experimental Validation of Model	183
18.4 Summary	184
References	184
Chapter 19 Comparison of Modal Parameters Extracted Using MIMO, SIMO, and Impact Hammer Tests on a Three-Bladed Wind Turbine	185
19.1 Introduction	185
19.2 Theoretical Background	186
19.2.1 Shaker Test with the Input Oblique to the Global Coordinate System	186
19.3 Structure Description and Test Setup	187
19.4 Test Cases Studied	189
19.4.1 Case 1: Impact Hammer Modal Test on the Fixture	189
19.4.2 Case 2: MIMO Test on the Wind Turbine Assembly	190
19.4.3 Case 3: SIMO Test on the Wind Turbine Assembly	191
19.4.4 Case 4: Modal Impact Hammer Test on the Wind Turbine Assembly	192
19.5 Discussion	192
19.5.1 Discussion 1: MIMO–SIMO Comparison	192
19.5.2 Discussion 2: Location of the Shakers	194
19.5.3 Discussion 3: Comparing the Modal Parameters Extracted using SIMO, MIMO, and Impact Tests	194
19.6 Observation	195
19.7 Conclusion	196
References	197
Chapter 20 Modal Test Results of a Ship Under Operational Conditions	198
20.1 Introduction	198
20.2 Experimental Setup	199
20.2.1 The Vessel	199
20.2.2 Measurement Equipment and Setup	200
20.2.3 Measurement Conditions	201
20.3 Results/Experimental Modal Analysis (Output-Only)	201
20.3.1 Cruising Condition	202
20.3.2 Anchor Condition	204
20.4 Conclusions and Future Work	205
References	205
Chapter 21 Measuring Effective Mass of a Circuit Board	206
21.1 Motivation and Application	207
21.2 Effective Mass Concept and History	207
21.3 Effective Mass Measurement Approach	208
21.4 Abbreviated Effective Mass Measurement Theory	209
21.5 Modal Test of Fixture with Truth Plate	209
21.6 Finite Element Model Truth Calculations	210
21.7 Experimental Effective Mass Extractions	212
21.8 Test Anomaly	212
21.9 Effective Mass of Circuit Board	214
21.10 Conclusions	214
References	216
Chapter 22 Acoustic Cavity Modal Analysis for NVH Development of Road Machinery Cabins	217
22.1 Introduction	217
22.2 Analytical Acoustic Description of a Cavity	218
22.3 FEA Calculation	219
22.4 Physical Acoustic Cavity Characterization	219
22.5 Results and Discussion	220
22.5.1 Feasibility of Rigid-Walled Assumption in Predicting Acoustic Cavity Modal Characteristics of the Cab In-Situ	220
22.5.2 Impact of the Seat and Steering Column on Experimental Acoustic Modal Parameters	221
22.5.3 Local Vibro-Acoustic Behavior and Its Relation to the Low Frequency Booming Event	224
22.6 Conclusion	228
References	229
Chapter 23 Strain-Based Dynamic Measurements and Modal Testing	230
23.1 Introduction	230
23.2 Theoretical Background	231
23.3 Experimental Analysis	232
23.3.1 Wind Turbine Blade	232
23.3.2 Composite T-Beam	234
23.3.3 Helicopter Main Rotor Blade	236
23.4 Results Analysis and Conclusion	237
References	238
Chapter 24 AIRBUS A350 XWB GVT: State-of-the-Art Techniques to Perform a Faster and Better GVT Campaign	240
24.1 Introduction	240
24.2 Airbus A350-XWB-900 Description	241
24.3 GVT General Specifications	242
24.4 GVT Equipments	242
24.5 GVT Teams	244
24.6 GVT Methods Applied	244
24.6.1 Data Work Flow	245
24.6.2 Modal Identification	245
24.7 ONERA DLR Specific Tools	246
24.7.1 Force Notching	246
24.7.2 SVDP: Single Virtual Driving Point	246
24.7.3 Modal Model Assembly	247
24.7.4 PRM Environment	248
24.8 Results	248
24.9 Conclusions	250
References	253
Chapter 25 Bayesian System Identification of MDOF Nonlinear Systems Using Highly Informative Training Data	254
25.1 Introduction	254
25.2 Bayesian Framework	255
25.3 Informative Training Data	256
25.4 Potential Issues	257
25.4.1 Most Probable Parameter Estimates	257
25.5 Nonlinear System	257
25.6 Results	258
25.7 Conclusions	260
References	262
Chapter 26 Finite Element Model Updating Using the Separable Shadow Hybrid Monte Carlo Technique	263
26.1 Introduction	263
26.2 Finite Element Model Background	264
26.3 Bayesian Inferences	264
26.4 The Hybrid Monte Carlo Method	266
26.5 The Separable Shadow Hamiltonian Function	267
26.6 The Modelled Structure and FE Model	268
26.7 Conclusion	269
References	271
Chapter 27 Bayesian System Identification of Dynamical Systems Using Reversible Jump Markov Chain Monte Carlo	272
27.1 Introduction	272
27.2 Bayesian Inference	273
27.3 MCMC Sampling Methods	274
27.4 RJMCMC	274
27.4.1 Detailed Balance and MH Sampler	276
27.4.2 Detailed Balance and RJMCMC	277
27.5 Conclusions	278
References	279
Chapter 28 Assessment and Validation of Nonlinear Identification Techniques Using Simulated Numerical and Real Measured Data	280
28.1 Introduction	280
28.2 A Review of the Selected Methods	281
28.2.1 Reverse Path Method (RP)	281
28.2.2 Frequency-domain Nonlinear Subspace Identification Method (FNSI)	283
28.3 Simulated Numerical Results	283
28.4 Real Measured Data Results	287
28.5 Conclusions and Future Work	290
References	293
Chapter 29 Effects of Errors in Finite Element Models on Component Modal Tests	294
29.1 Introduction	295
29.2 Development and Procedure of Dynamic Characteristics Prediction of Structures	296
29.2.1 Indication to Predict Target Frequency and Mode of Structures	296
29.2.2 Modeling Error Reduction	297
29.2.3 Target Frequency Error Estimation	299
29.3 Numerical Examples	300
29.3.1 Frequencies	301
29.3.2 System Identification of Tested Components	302
29.3.3 Dynamic Characteristics After Reducing Modeling Errors	304
29.3.4 Effect of Different Modeling Errors on Identified Results	306
29.4 Conclusions	306
References	306
Chapter 30 Estimating Frequency-Dependent Mechanical Properties of Materials	308
30.1 Introduction	309
30.2 Theory	309
30.2.1 Complex (Frequency-Domain) Material Properties	309
30.2.2 One-Dimensional Wave Propagation in a Bar	310
30.2.3 Semi-Infinite Two-Bar System	311
30.3 Experiment	313
30.4 Analysis	314
30.4.1 Estimation of Parameterized Frequency Distribution	315
30.5 Future Work	316
30.6 Summary	318
References	318
Chapter 31 Flexible Dynamic Modeling of Turret Systems by Means of Craig-Bampton Method and Experimental Validation	319
31.1 Introduction	319
31.2 Theory	321
31.3 Turret Case Study	322
31.3.1 Prototype Modal and Torque Frequency Sweep Tests	322
31.3.1.1 Barrel, Elevation and Azimuth Chassis Modal Tests	323
31.3.1.2 Torque Frequency Sweep Test	324
31.3.2 Two-Mass System Model	324
31.3.3 Flexible Dynamic Analysis	326
31.3.3.1 Model Preparation	326
31.3.3.2 Machine Elements Flexibilities	327
31.3.3.3 Simulation Results	328
31.4 Conclusion	330
References	332
Chapter 32 Material Characterization of Gyroscope Isolator Using Modal Test Data	333
32.1 Introduction	333
32.2 Methodology	334
32.3 Gyroscope A	334
32.3.1 Preliminary Modal Tests	334
32.3.2 FEM Model	335
32.3.3 Updated Modal Tests	336
32.4 Updated FEM and Material Properties	338
32.5 Gyroscope B	339
32.5.1 Modal Tests	340
32.5.2 FEM Model with Preset Material Properties	340
32.5.3 Sweep Tests and FRFS	340
32.6 Conclusion	342
References	344
Chapter 33 Loss Factors Estimation Using FEM in Statistical Energy Analysis	345
33.1 Introduction	345
33.2 Theory	346
33.3 SEA Models	347
33.3.1 Test Object	347
33.3.2 The SEA Subsystems	347
33.3.3 Estimation Method of SEA Parameter	348
33.4 Excitation of the Two Subsystems Connected Using Bolts	349
33.5 The Construction of the Finite Element Model	349
33.5.1 Test Equipment	350
33.5.2 FE Model of Panel and Base	351
33.5.3 The FE Model of the Coupled Subsystems	352
33.6 Conclusions	353
References	353
Chapter 34 Investigation of Crossing and Veering Phenomena in an Isogeometric Analysis Framework	354
34.1 Introduction	354
34.2 The Experimental Test-Rig	356
34.3 Nurbs-Based IGA and Test-Rig Model	357
34.4 Nitsche's Method for Domain Coupling	359
34.5 Parametric Modal Analysis and Results	361
34.6 Updating with Inverse Eigensensitivity Approach	365
34.7 Conclusions	368
References	368
Chapter 35 Influence of Fan Balancing in Vibration Reduction of a Braking Resistor	370
35.1 Introduction	370
35.2 Tested Braking Resistors	371
35.3 Modal Analysis of the Braking Resistor	371
35.4 Experimental Tests and Set-Up	372
35.5 Mechanical Impedance of the Supporting Structure	373
35.6 Assessment of the Constraint Forces at the Mounting Points of the Braking Resistor	374
35.7 Concluding Remarks	377
References	377
Chapter 36 Vibrations of Discretely Layered Structures Using a Continuous Variation Model	378
36.1 Introduction	379
36.2 Basic Problem	379
36.3 Transfer Matrix Approach	379
36.3.1 Frequencies	380
36.3.2 Mode Shapes	381
36.3.3 Numerical Example	382
36.4 Continuous Variation Model	382
36.4.1 Finite Difference Approach	383
36.4.2 Forced Motion Approach	384
36.5 Comparisons	386
36.6 Conclusions	389
References	389
Chapter 37 Next-Generation Random Vibration Tests	390
37.1 Introduction	390
37.2 Objectives	391
37.3 Case Study: Underwing Missile	391
37.4 The Flight Trial	392
37.5 The Twin-Shaker Single-Axis Vibration Test	393
37.6 Impedance Matched Multi-Axis Test (IMMAT)	396
37.7 Discussion and Conclusions	396
A.1 Appendix 1: Twin-Shaker Vibration Test Results	390
A.2 Appendix 2: IMMAT Results	391
References	403
Chapter 38 Optimal Phasing Combinations for Multiple Input Source Excitation	404
38.1 Introduction	404
38.2 Number of Sources Equal to Number of Phase Cases	405
38.3 Number of Sources Less than Number of Phase Cases	406
38.4 Phase Variation	407
38.5 Examples	407
38.5.1 Pseudo Random	407
38.5.2 Burst Chirp (Fast Sweep)	408
38.6 Summary	408
References	409

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