Dynamics of Coupled Structures, Volume 4

Preface	6
Contents	8
1 Verification of Experimental Component Mode Synthesis in the Sierra Analysis Framework	11
Nomenclature	11
1.1 Introduction	11
1.2 Craig-Mayes Experimental Sub-Structuring Method	12
1.3 Interface of Experimental CMS Model to Sierra	12
1.4 Demonstration	13
1.4.1 Configuration	13
1.4.2 Results	13
1.5 Conclusions	15
References	15
2 Multi-DoF Interface Synchronization of Real-Time-Hybrid-Tests Using a Recursive-Least-Squares Adaption Law: A Numerical Evaluation	16
2.1 Introduction	16
2.2 Hybrid Testing Problem Formulation	17
2.3 Adaptive Feedforward Algorithm	19
2.4 Numerical Case Study	20
2.5 Conclusion	21
References	23
3 Controls Based Hybrid Sub-Structuring Approach to Transfer Path Analysis	24
3.1 Introduction	24
3.2 Real Time Hybrid Substructuring	25
3.3 Controls Approach to Transfer Path Hybrid Substructuring	26
3.3.1 Physical Loading Using Auto Power Spectral Densities	27
3.4 Numeric Example	28
3.5 Experimental Example	31
3.6 Conclusion	32
References	33
4 Force Identification Based on Subspace Identification Algorithms and Homotopy Method	34
4.1 Introduction	34
4.2 System Identification Based on Subspace Identification Algorithm	35
4.3 The Force Identification Model	36
4.4 Practical Application	37
4.5 Conclusions	39
References	40
5 Response DOF Selection for Mapping Experimental Normal Modes-2016 Update	41
5.1 Introduction	41
5.2 Nomenclature	42
5.3 Understanding Normal Modes	42
5.4 Model Order Reduction Strategies	43
5.4.1 Classic Guyan Reduction	43
5.4.2 Modified Guyan Reduction	44
5.4.3 General Model Order Reduction	45
5.5 Reduced Order Model Orthogonality and Residual Kinetic Energy	45
5.6 Branched Shell Illustrative Example	46
5.6.1 Model Description and Dynamic Characteristics	46
5.6.2 Allocation of instrumented DOFS (Accelerometers)	47
5.6.3 TAM Definition Using “Classical” Guyan Reduction	48
5.6.4 TAM Definition Using “Modified” Guyan Reduction	49
5.6.5 Further Reflections on “Modified” Guyan Reduction Results	51
5.7 Concluding Remarks	51
A.1 Appendix: Exploitation of Generalized Modal Data	52
References	54
6 Experimental Modal Substructuring with Nonlinear Modal Iwan Models to Capture Nonlinear Subcomponent Damping	55
6.1 Introduction	55
6.2 Theoretical Development	56
6.2.1 Iwan Joint	57
6.3 Simulated Application	58
6.3.1 Estimating Modal Iwan Models for Substructure A	58
6.3.2 Substructuring Predictions	60
6.4 Conclusions	61
References	63
7 A Modal Model to Simulate Typical Structural Dynamic Nonlinearity	64
Nomenclature	64
7.1 Introduction and Motivation	65
7.2 Experiment	66
7.2.1 Hardware Description	66
7.2.2 Test Set-Up	66
7.2.3 Preliminary Modal Results	68
7.3 Signal Processing	68
7.3.1 Modal Filtering	69
7.3.1.1 SMAC Modal Filter	69
7.3.1.2 Full Modal Filter	69
7.3.1.3 Single Modal Filter	69
7.3.1.4 Modal Filter Results and Comparison	70
7.3.2 Hilbert Transform and Band-Pass Sensitivity	70
7.4 Nonlinear Models	72
7.4.1 Modal Iwan Model	72
7.4.2 FREEVIB	74
7.4.3 Restoring Force Surface	75
7.5 Results and Observations	77
7.5.1 Simulation Results and Observations	77
7.5.2 Discussion	80
7.6 Conclusions	81
7.6.1 Nonlinear Pseudo-Modal Model Assumptions	81
7.6.2 Nonlinear Pseudo-Modal Model Testing Approach	81
7.6.3 Signal Pre-Processing with Modal Filter, Band Pass Filter and Hilbert Transform	81
7.6.4 Nonlinear Pseudo-Modal Model Forms	82
References	83
8 Optimal Replacement of Coupling DoFs in Substructure Decoupling	84
8.1 Introduction	84
8.2 Direct Decoupling Using Dual Assembly	85
8.2.1 Disconnection Force Intensities Provided by Dual Assembly	86
8.2.2 FRF and Transmissibility Indicators	87
8.2.3 Prediction of the FRF of the Unknown Subsystem	89
8.3 Test Bed	89
8.3.1 Analysis of FRF and Transmissibility Indicators	91
8.3.2 Decoupling	92
8.4 Concluding Remarks	96
References	96
9 State-Space Substructuring with Transmission Simulator	98
9.1 Introduction	98
9.2 Theory	99
9.3 Experiments and System Identification	102
9.3.1 Experimental Setup	102
9.3.2 System Identification and FE Models	103
9.3.3 Identified Models	104
9.4 Substructuring Results	106
9.5 Discussion	107
9.6 Concluding Remarks	109
References	109
10 Applying the Transmission Simulator Techniques to the Ampair 600 Wind Turbine Testbed	111
10.1 Introduction	111
10.2 Theoretical Development of the Transmission Simulator	112
10.2.1 Uncoupled Equation of Motion	112
10.2.2 Transmission Simulator Models	112
10.2.2.1 Free-Free Modal Transmission Simulator Model	113
10.2.2.2 Craig-Bampton Transmission Simulator Model	113
10.2.3 Coupling Procedures	113
10.2.3.1 Modal Constraints (MCFS)	114
10.2.3.2 MCFS for Free-Free Transmission Simulator (MCFS-FF)	114
10.2.3.3 Motion Relative to the Interface (CB-IP)	115
10.3 Modeling of the Wind Turbine Rotor Assembly	116
10.4 Numerical Study of the Hub-one-Blade System	118
10.4.1 Free-Free Modes of the Blade B̃	118
10.4.2 Fixed-Free Modes of the Blade B̃	119
10.4.3 Assembly of the Rotor System	119
10.5 Conclusion	121
References	121
11 Effect of Interface Substitute When Applying Frequency Based Substructuring to the Ampair 600 Wind Turbine Rotor Assembly	122
11.1 Introduction	122
11.2 Test Setup	123
11.3 Substructuring Methodology	124
11.4 Results	125
11.5 Conclusion	126
References	127
12 Improving Floor Vibration Performance Using Interstitial Columns	128
12.1 Introduction	128
12.2 Vibration Criteria	128
12.3 Case Study #1: Long Span Steel Fitness Floor	129
12.4 Case Study #2: Office to Laboratory Conversion	131
12.5 Case Study #3: Disappearing Partitions	132
12.6 Conclusions	133
References	134
13 Probabilistic Model Updating of Controller Models for Groups of People in a Standing Position	135
13.1 Introduction	135
13.2 Methodology	136
13.2.1 Structural Model (G(s))	136
13.2.2 Human Model (H(s))	136
13.2.3 Model Updating	137
13.3 Experimental Setup	137
13.4 Results	138
13.4.1 Parameters of the Structure	138
13.4.2 Human-Structure Interaction for a Single Human	139
13.4.3 Human-Structure Interaction for Groups of Two People	139
13.5 Conclusions	139
References	140
14 Fundamental Frequency of Lightweight Cold-Formed Steel Floor Systems	141
14.1 Introduction	141
14.2 Prediction of the Fundamental Frequency of Partially Restrained Orthotropic Plate by Rayleigh-Ritz Method	142
14.3 Equivalent Orthotropic Plate for CFS Floor Systems	144
14.3.1 Equivalent Rigidity Properties of CFS Floor Systems	144
14.3.2 Simplified Equations for Equivalent Rigidity Properties	146
14.3.3 Discussion	148
14.4 Conclusion	148
References	149
15 Fundamental Studies of AVC with Actuator Dynamics	150
15.1 Introduction	150
15.2 Ideal Direct Velocity Feedback	151
15.3 Effect of Actuators and Filters	153
15.4 Conclusions	156
References	157
16 Mitigating Existing Floor Vibration Issues in a School Renovation	158
16.1 Introduction	158
16.2 Analytical Investigation	158
16.3 Experimental Testing	159
16.4 Interpretation of Results	160
16.5 Recommendations to Mitigate Excessive Vibration Levels	164
References	165
17 Vibration Serviceability Assessment of an In-Service Pedestrian Bridge UnderHuman-Induced Excitations	166
17.1 Introduction	166
17.2 Description of Footbridge	167
17.3 Finite Element Simulation	167
17.4 Test Set-Up and Instrumentation	168
17.5 Dynamic Tests Conducted on the Footbridge	168
17.5.1 Ambient Vibration Tests	168
17.5.2 Pedestrian Interaction Tests	169
17.6 Modal Identification Using Frequency Domain Decomposition	171
17.7 Evaluation of Pedestrian Interaction Test Results	171
17.8 Conclusions	174
References	174
18 Numerical and Experimental Studies on Scale Modelsof Lightweight Building Structures	176
18.1 Introduction	176
18.2 Governing Theory	176
18.3 Scale Models of Building Structures	177
18.3.1 Example: Wooden Building Structure	178
18.4 Concluding Remarks	182
References	183
19 A Wavelet-Based Approach for Generating Individual Jumping Loads	184
19.1 Introduction	184
19.2 Jumping Load Data Collection	185
19.3 Model Parameters	186
19.3.1 Time Interval OF Jumping Cycle: Ti	187
19.3.2 Contact Ratio: αi	187
19.4 Wavelet Analysis of Jumping Impulses	189
19.4.1 Basis of Wavelet Analysis [28, 29]	189
19.4.2 Analysis OF Jumping Impulses	190
19.5 Stochastic Jumping Load Model and Verification	191
19.5.1 The Information Database of Wavelet Analysis	191
19.5.2 Stochastic Jumping Load Model	192
19.5.3 Model Verification	192
19.6 Conclusions	193
References	195
20 A Numerical Round Robin for the Prediction of the Dynamics of Jointed Structures	197
20.1 Introduction	197
20.2 The Benchmark Model	198
20.2.1 The Finite Element Mesh	198
20.3 Nonlinear Static Analysis	199
20.4 Considered Approaches to Modelling Friction Joints	200
20.4.1 Sandia Approach	200
20.4.2 Stuttgart Approach	201
20.4.3 Imperial Approach	202
20.5 SDOF Comparison Between Nonlinear Elements	203
20.5.1 How Each Approach Calculates Damping	204
20.5.2 SDOF Comparison Results	205
20.6 Brake-Reuss Beam Nonlinear Dynamic Anlaysis	206
20.6.1 Reduced Interface Frequency Response Analysis	206
20.6.2 Full Interface Analysis	207
20.6.3 Tuning the Iwan Element Joint Model Using Amplitude-Dependent Damping	208
20.7 Conclusion	212
References	213
21 A Method to Capture Macroslip at Bolted Interfaces	214
Nomenclature	214
21.1 Introduction	214
21.2 Test Setup	215
21.3 Test Results	217
21.4 Analysis Approach	224
21.5 Analysis Results	225
21.5.1 Analysis Results, 63 G Peak Acceleration	225
21.5.2 Analysis Results, 89 G Peak Acceleration	226
21.5.3 Analysis Results, 125 G Peak Acceleration	227
21.6 Summary	228
References	230
22 A Reduced Iwan Model that Includes Pinning for Bolted Joint Mechanics	231
22.1 Introduction	231
22.2 Analytical Development	232
22.2.1 Pinning Force	232
22.2.1.1 Relation of Relative and Global Displacements for the Iwan and Pinning Forces	233
22.2.2 Four-Parameter Iwan Model Overview	233
22.2.2.1 Considerations for Cyclic Loading	236
22.2.2.2 Comparison with the Discrete Four-Parameter Iwan Model	237
22.2.3 Extension to the Five-Parameter Iwan Model	238
22.2.4 Extension to the Uniform Iwan Distribution	239
22.3 Summary	239
References	240
23 Nonlinear Vibration Phenomena in Aero-Engine Measurements	241
23.1 Introduction	241
23.2 Nonlinearity in Measured Data	242
23.3 Component Level	243
23.3.1 Sub-System Level	243
23.3.2 System Level	245
23.4 Assessment of Nonlinear Responses	248
23.5 Capability Requirements	250
23.6 Conclusions	251
References	252
24 Instantaneous Frequency and Damping from Transient Ring-Down Data	253
24.1 Introduction	253
24.2 Theoretical Development	254
24.2.1 Short Time Fourier Transform with Time Varying Window	254
24.2.2 Parameter Estimation from Ring-Down	256
24.3 Numerical Results: Multi-DOF Nonlinear Beam	257
24.3.1 Initial Conditions of NNM	257
24.3.2 Broadband Excitation	258
24.4 Experimental Results: Beam with Bolted Lap Joint	260
24.5 Conclusion	262
References	262
25 Explicit Modelling of Microslip Behaviour in Dry Friction Contact	264
25.1 Introduction	264
25.2 Friction Test Rig	265
25.3 Finite Element Modelling	265
25.4 Results	267
25.4.1 Experimental Results	267
25.4.2 Finite Element Results	268
25.4.2.1 Pressure Distribution	268
25.4.2.2 Tangential Contact Stiffness	268
25.4.2.3 Microslip	269
25.5 Conclusion	270
References	271
26 Modal Testing Through Forced Sine Vibrations of a Timber Footbridge	272
26.1 Introduction	272
26.2 Marecchia River Footbridge	273
26.3 Forced Vibration Tests	273
26.4 Frequency Response Functions (FRFs)	275
26.5 Modal Identification	276
26.6 Conclusions	279
References	279
27 Damping Characteristics of a Footbridge: Mysteries and Truths	281
27.1 Introduction	281
27.2 The Bridge	282
27.3 Experimental Modal Analysis of the Structure Under Ambient Excitation	282
27.3.1 Test Strategy	282
27.3.2 Results from Signal Processing of the Data	283
27.3.3 Dynamic Loading Tests	285
27.4 The Michael Mistler Paper	285
27.5 Damping as a Function of Frequency Resolution: EFDD	286
27.6 Damping Estimation in the Time Domain	288
27.7 Comparison of Identification Techniques for Damping Estimation	289
27.8 Summary	289
References	289
28 A Critical Analysis of Simplified Procedures for Footbridges' Serviceability Assessment	291
28.1 Introduction	291
28.2 Unrestricted Pedestrian Traffic: Approximate Evaluation of the Maximum Dynamic Response	292
28.3 Numerical Validation of the Approximate Procedures	293
28.4 Technical Considerations	295
28.5 Concluding Remarks	295
References	296
29 Human-Induced Vibrations of Footbridges: The Effect of Vertical Human-Structure Interaction	297
29.1 Introduction	297
29.2 The Moving Crowd Model	298
29.2.1 The Supporting Structure	298
29.2.2 The Pedestrians	298
29.2.3 Stiff Supporting System	299
29.2.4 Flexible Supporting System	299
29.2.5 Response Calculation	300
29.3 Crowd Flow Model	301
29.4 Impact HSI	302
29.4.1 Input Parameters	302
29.4.2 Output Quantities of Interest	302
29.4.3 Results	302
29.4.3.1 Evaluation of the Structural Response	303
29.4.3.2 Impact of HSI	303
29.5 Conclusions	304
References	304
30 Nonlinear Time-Varying Dynamic Analysis of a Multi-Mesh Spur Gear Train	306
Nomenclature	306
Subscripts	307
Superscripts	307
30.1 Introduction	307
30.2 Dynamic Model Formulation	308
30.2.1 Physical System and Dynamic Model	308
30.2.2 Period-One Dynamics	310
30.2.3 Loading Conditions and Mesh Phases	312
30.3 Results and Discussion	314
30.4 Conclusion	317
References	317
31 Energy Dissipation of a System with Foam to Metal Interfaces	319
31.1 Introduction	319
31.2 Experimental Setup	320
31.2.1 Foam Specimen Details	320
31.2.2 Solid Mass Details	321
31.2.3 Specimen Assembly	321
31.2.4 Test Specifications and Data Collection	321
31.3 Experimental Results	322
31.3.1 Effects of Amplitude of Excitation	322
31.3.2 Effects of Snugness of Fit	322
31.4 Numerical Results	326
31.4.1 Computational Model	326
31.4.2 Comparison Between Model and Experiments	327
31.5 Conclusions	327
References	328
32 Nonlinear System Identification of Mechanical Interfaces Based on Wave Scattering	329
32.1 Introduction	329
32.2 Problem Formulation	330
32.3 Nonlinear System Identification	331
32.3.1 Preloaded Clearance Interface	331
32.3.2 Frictional Interface	332
32.4 Concluding Remarks	333
References	334
33 Studies of a Geometrical Nonlinear Friction Damped System Using NNMs	336
33.1 Introduction	336
33.2 The Concept of Nonlinear Normal Modes	336
33.3 Investigation of a Frequency-Energy-Independent Geometrically Nonlinear System	337
33.3.1 Definition of the Numerical Model	337
33.3.2 Proposed Methodology	338
33.3.2.1 Finding an Isolated Resonance	339
33.3.2.2 Autonomous Decay Process with Damping Identification	339
33.3.2.3 Identification of Frequency-Independent System Configuration	340
33.4 Numerical Results	340
33.5 Conclusion	343
References	343
34 Scale-Dependent Modeling of Joint Behavior	344
34.1 Introduction	344
34.2 Constitutive Contact Laws	344
34.2.1 Rough Surface	344
34.2.2 Constitutive Contact Laws	345
34.2.2.1 Normal Behavior	346
34.2.2.2 Tangential behavior	346
34.3 Simple Joint Model	347
34.4 Parameter Identification	348
34.5 Reduced Model	348
34.6 Conclusion	349
References	350
35 Robust Occupant Detection Through Step-Induced Floor Vibration by Incorporating Structural Characteristics	352
35.1 Introduction	352
35.2 Literature Survey	353
35.3 Occupant Detection Algorithm Using Structural Characteristics	354
35.3.1 Structure Characterization	355
35.3.2 Occupant Footstep Detection	356
35.3.2.1 Event Detection	357
35.3.2.2 Event Classification on Detected Events	357
35.4 Evaluation	357
35.4.1 Description of Experiments	358
35.4.2 Results and Discussion	358
35.4.2.1 Baseline Method	359
35.4.2.2 Event Detection Module	360
35.4.2.3 Event Classification Module	360
35.5 Future Work	360
35.6 Conclusions	361
References	361
36 Assessment of Large Error Time-Differences for Localization in a Plate Simulation	363
36.1 Introduction	363
36.2 Modeling and Simulation of Source Localization	364
36.3 Results and Discussion	366
36.4 Conclusion	369
References	369
37 Gender Classification Using Under Floor Vibration Measurements	371
37.1 Introduction	371
37.2 Experimental Setup	372
37.3 Data Representation	373
37.4 Machine Learning Technique	374
37.5 Results	375
37.6 Conclusions	376
References	377
38 Human-Structure Interaction and Implications	378
Nomenclature	378
38.1 Introduction	378
38.2 Experiments	379
38.2.1 The Test Floor	379
38.2.2 Tests on the Empty Floor	379
38.2.3 Further Tests on the Floor	379
38.2.4 Results	380
38.2.5 Discussion	381
38.3 Numerical Case Study	381
38.3.1 The Interaction Model	381
38.3.2 The Load Model	381
38.3.3 Calculated Floor Response and Results	382
38.4 Conclusion and Discussion	382
References	382
39 Study of Human-Structure Dynamic Interactions	383
39.1 Introduction	383
39.2 Description of the Test Structure	384
39.3 Modal Testing	385
39.4 Vibration Tests with Human Subjects	385
39.5 Estimation of the Human Dynamic Properties	388
39.6 Verification of the Identified Human Dynamic Parameters	389
39.7 Summary and Conclusions	390
References	390
40 Characterisation of Transient Actions Induced by Spectators on Sport Stadia	392
40.1 Introduction	392
40.2 Human-Induced Vibrations on Stadia	393
40.3 Inverse Force Reconstruction from Structural Responses	393
40.4 Laboratory Testing	395
40.4.1 Experimental Testing Methodology	395
40.5 Results and Discussion	397
40.6 Conclusions	399
References	399
41 Recent Issues on Stadium Monitoring and Serviceability: A Review	401
41.1 Introduction	401
41.2 Load Modeling	402
41.3 Human Structure Interaction	403
41.4 Perception and Human Comfort	404
41.5 Conclusions	404
References	405
42 Characterising Randomness in Human Actions on Civil Engineering Structures	407
42.1 Introduction	407
42.2 Experiments on Rigid Surface	408
42.3 Data Processing	408
42.4 Randomness of Key Parameters	409
42.4.1 Walking	409
42.4.2 Jumping	409
42.5 Experiments on Lively Surface	410
42.5.1 WB Description and Test Setup	410
42.5.2 Randomness on Lively Bridge	412
42.6 Sensitivity of Vibration Response	413
42.7 Conclusions	413
References	414
43 Optimal Restraint Conditions for the SID-IIs Dummy with Different Objective Functions	415
43.1 Introduction	415
43.2 Formulation of the Optimal Problem	416
43.2.1 A Spring-Mass Model for the SID-IIs	416
43.2.2 Formulation of the Multi-Objective Optimal Restraint Problem	417
43.3 Numerical Results	419
43.3.1 Weighting Vector w==[1 0 0]	420
43.3.2 Weighting Vector w==[0 0 1]	421
43.3.3 Weighting Vector w==[0 0.5 0.5]	421
43.3.4 Maximum Compliance Margin Numerical Example	422
43.4 Discussion	423
43.5 Conclusion	426
References	427
44 A Comparison of Common Model Updating Approaches	428
44.1 Introduction	428
44.2 Common Model Updating Techniques	429
44.2.1 Model Updating Methods Using Modal Data	429
44.2.2 Model Updating Methods Using Frequency Response Data	429
44.3 Measurement	430
44.4 Modeling	430
44.5 Model Updating	430
44.6 Results	432
44.7 Conclusion	433
References	435
45 Experimental Coupling and Decoupling of Engineering StructuresUsing Frequency-Based Substructuring	436
45.1 Introduction	436
45.2 Theoretical Background	437
45.2.1 Frequency-Based Substructuring Using the Dual Formulation	437
45.2.2 Numerical Improvements of the General Methods	439
45.3 Experimental Data Analysis	440
45.3.1 Measured FRFs Analysis	441
45.3.2 Decoupling Results	442
45.3.3 Improved FRFs for Decoupling	445
45.3.3.1 Decoupling Using Synthesized Input FRFs	445
45.3.3.2 Decoupling Imposing Reciprocity on Input FRFs	446
45.3.3.3 Decoupling Imposing Synthesized FRFs with the ML-MM Method	447
45.4 Conclusions	449
References	449
46 New FRF Based Methods for Substructure Decoupling	451
46.1 Introduction	451
46.2 Theory	452
46.2.1 Formulation Using Equation (46Equ946.9)	453
46.2.2 Formulation Using Equation (46Equ1046.10)	454
46.3 Case Studies	455
46.3.1 Application of the Approaches to a Lumped Parameter System	455
46.3.2 A Comparison of the Approaches with Well-Known Existing Methods	457
46.4 Discussion and Conclusions	459
References	459
47 Experimental Determination of Frictional Interface Models	461
47.1 Introduction and Background	461
47.2 Proposed Joint Models	462
47.2.1 Coulomb Friction	462
47.2.2 Jenkins Element	462
47.2.3 Iwan Element	463
47.3 Experimentation	464
47.3.1 Impact Hammer Testing	464
47.3.1.1 Experimental Setup	464
47.3.1.2 Test Data and Preliminary Analysis	465
47.3.2 Profile Testing	465
47.3.2.1 Experimental Setup	466
47.3.2.2 Reasoning	467
47.3.2.3 Test Data	467
47.4 Joint Model Parameter Estimation	469
47.4.1 Theory and Background	470
47.4.2 Parameter Distributions	473
47.5 Plasticity Effects	474
47.6 Conclusions	476
References	478
48 Effects of Experimental Methods on the Measurements of a Nonlinear Structure	479
48.1 Introduction	479
48.2 Experimental Setups	481
48.3 Control Parameter	482
48.4 Repeatability Experiments	486
48.5 Conclusions	486
References	488
49 Stress Waves Propagating Through Bolted Joints	489
49.1 Introduction	489
49.2 Approach	490
49.3 Bolt Load	491
49.3.1 Residual Stress	492
49.4 Shock Loading	493
49.4.1 Types of Dissipative Responses	493
49.4.2 Results	493
49.5 Discussion	495
49.6 Conclusion	496
References	497
50 A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring	498
50.1 Introduction and Motivation	498
50.2 Theory	499
50.2.1 Transmission Simulator	499
50.2.2 Craig-Bampton	500
50.2.3 Craig-Mayes	501
50.2.4 Craig-Chang Reduction Method	502
50.2.5 Dual Craig-Bampton Method	503
50.3 Simple Beam System	504
50.3.1 Substructuring Example	504
50.3.2 Condition of Substructuring	505
50.4 Cylinder-Plate-Beam System	507
50.4.1 Introduce System	507
50.4.1.1 Experiment	509
50.4.1.2 Model	509
50.4.2 Predictions and Comparison with Experimental Truth Data	511
50.4.2.1 Traditional TS Method	512
50.4.2.2 Craig-Mayes Method	513
50.4.2.3 Observations and Comparison of Traditional TS Method and Craig-Mayes Method	514
50.5 Conclusions	515
References	515

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