Dynamics of Coupled Structures, Volume 1

Preface	6
Contents	8
1 Experimental-Analytical Dynamic Substructuring of Ampair Testbed: A State-Space Approach	11
1.1 Introduction	11
1.2 Theory	12
1.2.1 System Identification	12
1.2.2 Substructuring	13
1.2.3 State-Space Coupling	13
1.2.3.1 General Framework	14
1.2.3.2 Second Order Form Equivalent of Synthesised First Order Form	14
1.3 Analytical Models	16
1.3.1 Blade	16
1.3.2 Bracket	17
1.3.3 FE Coupling	17
1.4 Experiments	18
1.4.1 Test Setup	19
1.5 Experimental Models	20
1.6 Results	20
1.6.1 Analytical and Synthesised Blade Models	21
1.6.2 Blade Bracket	21
1.7 Conclusions and Further work	22
References	23
2 Experimental Dynamic Substructuring of the Ampair Wind Turbine Test Bed	25
2.1 Introduction	25
2.2 Coupling and Decoupling in the Frequency Domain	26
2.2.1 Addition of Subsystems	26
2.2.1.1 Dual Formulation in the Frequency Domain DRV08	27
2.2.2 Subtraction of Subsystems Using the Dual Domain Decomposition [6]	28
2.3 Test Structure	29
2.4 Experimental Dynamic Substructuring	30
2.4.1 Experimental Data Description	30
2.4.2 Response Selection and Curve Fitting	31
2.4.3 Synthesis of the Unmeasured FRF Elements	31
2.4.4 Coupling of the Blade with the Two Bladed Turbine and Mass Cancellation	34
2.5 Conclusions	34
References	35
3 Are Rotational DoFs Essential in Substructure Decoupling?	37
3.1 Introduction	37
3.2 Direct Decoupling Techniques	38
3.2.1 Dual Assembly	39
3.3 Test Structure	41
3.4 Decoupling	41
3.4.1 Results Without Added Noise	42
3.4.2 Results Using Raw FRFs with Added Noise of 0.05%	42
3.4.3 Results Using Fitted FRFs with Added Noise of 1%	44
3.5 Summary and Discussion	45
References	45
4 Validation of Blocked-Force Transfer Path Analysis with Compensation for Test Bench Dynamics	47
4.1 Introduction	47
4.1.1 Paper Outline	48
4.2 Theory	48
4.2.1 Substructured Response	48
4.2.2 Blocked-Force Response	50
4.2.3 Operational Response on Test Bench	50
4.2.4 Equivalent Forces from Inverse BF-TPA	51
4.3 Practice	52
4.3.1 Description of Collocated 6-DoF Motion and Loads	52
4.3.2 Determination of Non-measurable Interface Loads	53
4.3.3 Application: Determination of Interface Moments	54
4.4 Test Case	55
4.4.1 Determination of the Interface Loads	55
4.4.2 Composition of the Blocked Force	56
4.4.2.1 Blocked Force Using Inverse BF-TPA	56
4.4.3 BF-TPA Results	57
4.5 Conclusions	58
References	58
5 Prediction of Forced Response on Ancillary Subsystem Components Attachedto Reduced Linear Systems	60
5.1 Introduction	61
5.2 Theory	62
5.2.1 Equations of Motion for Multiple Degree of Freedom System	62
5.2.2 Structural Dynamic Modification	62
5.2.3 General Reduction/Expansion Methodology and Model Updating	63
5.2.3.1 Expansion of System Modes from Uncoupled Component Modes	64
5.2.3.2 System Equivalent Reduction Expansion Process (SEREP)	64
5.2.3.3 KM_AMI Reduction	64
5.2.4 System Forced Response Analysis	64
5.2.5 Time Response Correlation Tools	66
5.2.5.1 Modal Assurance Criterion (MAC)	66
5.2.5.2 Time Response Assurance Criterion (TRAC)	66
5.3 Model Description	67
5.4 Cases Studied	68
5.4.1 Case 1: Reference Model	70
5.4.1.1 Component Mode Contribution—U12	70
5.4.2 Overview of Reduced Models	71
5.4.3 Case 2: Guyan Reduced Model	71
5.4.4 Case 3: SEREP Reduced Model	74
5.4.5 Case 4: KM_AMI Model Improvement from Guyan Reduced Model	77
5.4.6 Case 5: Considerations for Additional Modes in the Model Reduction	77
5.4.7 Case 6: Considerations for DOF Selection in the Model Reduction	78
5.4.8 Observations	79
5.5 Conclusion	79
References	80
6 Towards Dynamic Substructuring Using Measured Impulse Response Functions	82
6.1 Introduction	82
6.2 Recap of IBS	83
6.2.1 Using Impulse Response Functions for Time Integration	83
6.2.2 Coupling of Impulse Response Functions by Means of Lagrange Multipliers	84
6.2.3 Which IRFs to Use: Displacement, Velocity or Acceleration IRFs?	85
6.3 Obtaining IRFs from Experiments	85
6.3.1 Frequency-Domain Approach	86
6.3.2 Time-Domain Approach	86
6.3.3 Inverse Filter Approach	88
6.3.4 Multiple Impact Averaging	89
6.3.5 Application to a POM Bar	90
6.4 Observations and Outlook	90
References	91
7 Hybrid Modeling of Floating Raft System by FRF-Based Substructuring Method with Elastic Coupling	92
7.1 Introduction	92
7.2 Influence of Rotational DOFs—A Simple Experiment	93
7.3 Possible Ways to Improve the Accuracy of DS Modeling	94
7.3.1 Experimental Set-Up to Identify the Rotational Mobility of Isolators	95
7.3.2 Filters to Condition the Numerical FRFs with the Measured FRFs	96
7.3.3 Truncated SVD to Eliminate Measurement Noise	97
7.4 Conclusion	98
References	98
8 Experimental Based Substructuring Using a Craig-Bampton Transmission Simulator Model	99
8.1 Introduction	99
8.2 Theoretical Development	100
8.2.1 Free-Free Modal Transmission Simulator (FF-TS)	100
8.2.2 Craig-Bampton Transmission Simulator	101
8.2.2.1 Method 1: Free Modes of Craig Bampton Model (CB-TS)	102
8.2.2.2 Method 2: Motion Relative to the Interface (CB-IP)	102
8.3 Numerical Examples	103
8.3.1 T-Beam System from [8CR1010]	104
8.3.2 Two-Dimensional Structure with Indeterminate Interface	106
8.3.2.1 Results for Assembly of Interest	108
8.4 Conclusion	110
References	112
9 Consideration of Interface Damping in Shrouded Mistuned Turbine Blades	113
9.1 Introduction	113
9.2 Component Mode Synthesis of the Turbine	114
9.2.1 Reduction of the Blade	114
9.2.2 Reduction and Cyclic Transformation of the Disk	115
9.2.3 Assembly and Interface Reduction	115
9.3 Mistuning	116
9.4 Coupling of the Shrouds	117
9.5 Harmonic Balance Method	118
9.6 Results	118
9.7 Conclusion	119
References	120
10 Coupling Elements for Substructure Modelling of Lightweight Multi-storey Buildings	121
10.1 Introduction	121
10.1.1 Timber Volume Elements	122
10.1.2 Objective	123
10.2 Governing Theory	124
10.2.1 Model Order Reduction	124
10.2.1.1 Component Mode Synthesis by Craig and Bampton	124
10.2.2 Interface Reduction	125
10.3 Elastomer Blocks as Coupling Elements	126
10.4 Test Model	128
10.5 Conclusions	131
References	131
11 Deformation Mode Selection and Orthonormalization for an Efficient Simulation of the Rolling Contact Problem	133
11.1 Introduction and Motivation	134
11.2 Craig-Bampton CMS Method	135
11.3 Extension of the Craig-Bampton Reduction Base with Characteristic Attachment Modes for Rolling Contact Problems	136
11.3.1 Attachment Modes	136
11.3.2 Characteristic Attachment Modes	136
11.3.3 Characteristic Attachment Modes for Rolling Contact Problems	137
11.4 Run-Up Simulation of Coupled System Between Working and Back-Up Roll	139
11.5 Conclusion	141
References	141
12 Towards a Parallel Time Integration Method for Nonlinear Systems	143
12.1 Introduction	143
12.2 Dynamic Simulations for Coupled Mechanical Systems	144
12.2.1 Coupling of the Equations of Motion	144
12.2.1.1 Primal Assembly	145
12.2.1.2 Dual Assembly	145
12.2.2 Time Integrating the Equations of Motion Using Newmark's Method	145
12.3 Decomposed Time Integrations	147
12.3.1 Decomposition into Global and Local Iterations	147
12.3.2 Benefits of Separating the Global and Local Iterations	148
12.4 Demonstration on a Simple Academic Model	149
12.4.1 The Simple Academic Model	149
12.4.2 Accuracy of the Proposed Method	150
12.4.3 Effect of Setting the Local and Global Tolerances	151
12.4.4 Effect of the Level of Nonlinearity in the Subsystems	152
12.5 Conclusions and Recommendations	153
References	153
13 Efficient Model Order Reduction for the Nonlinear Dynamics of Jointed Structures by the Use of Trial Vector Derivatives	154
13.1 Introduction	155
13.2 Theory	155
13.2.1 Trial Vector Derivatives	156
13.2.2 Proper Orthogonal Decomposition (POD) for the Computation of an Optimal Set of JIMs	157
13.3 Numerical Example	158
13.3.1 “Joint Interface Modes” Based on Trial Vector Derivatives	158
13.3.2 Static Response Computation	159
13.3.3 Dynamic Response Computation Without Friction	160
13.3.4 Dynamic Response Computation with Friction	160
13.3.5 Computational Efficiency	161
13.4 Conclusion	161
References	161
14 A Substructuring Method for Geometrically Nonlinear Structures	163
14.1 Introduction	163
14.2 Problem Formulation	164
14.2.1 Substructuring	164
14.2.2 Component Mode Synthesis	164
14.2.3 Craig–Bampton Method	165
14.2.4 Rubin Method	165
14.3 Modal Derivatives	166
14.4 Augmented Reduction Bases	167
14.5 Results	169
14.6 Conclusions and Future Directions	170
References	171
15 Craig-Bampton Substructuring for Geometrically Nonlinear Subcomponents	172
15.1 Introduction	172
15.2 Theoretical Development	174
15.2.1 Craig-Bampton Nonlinear Reduced Order Model	174
15.2.2 Coupling with Craig-Bampton Method	176
15.3 Numerical Results	177
15.3.1 Linear Substructuring Results	177
15.3.2 Validate Nonlinear Reduced Order Models	178
15.3.3 Nonlinear Substructuring Results	179
15.4 Conclusion	181
References	183
16 Parameterized Reduced Order Models Constructed Using Hyper Dual Numbers	184
16.1 Introduction	185
16.2 Craig-Bampton Component Mode Synthesis	186
16.3 Parameterization Using Hyper Dual Numbers	187
16.3.1 Derivatives of Eigenvalues and Eigenvectors	188
16.4 Application to a Stepped Beam	190
16.5 Conclusions and Future Work	194
References	197
17 Efficient Stochastic Finite Element Modeling Using Parameterized Reduced Order Models	198
17.1 Introduction	198
17.2 Parameterization Methods	199
17.2.1 Analysis Process	200
17.2.1.1 Parameterizing Full-DOF Component Matrices	200
17.2.1.2 Parameterizing C–B CMS Component Matrices	200
17.2.1.3 Parameterizing the Eigenvalues and Eigenvectors	201
17.3 Application of Parameterization Methods to an Example Finite Element Model	201
17.4 Discussion of Results	202
17.5 Conclusions and Future Work	205
References	206
18 Application of a Novel Method to Identify Multi-axis Joint Properties	207
18.1 Introduction	207
18.2 Problem Formulation	208
18.3 Direct Joint Identification	208
18.4 Inverse Joint Identification	208
18.5 Computational Model	209
18.6 Experimental Validation	210
18.7 Estimation of the Mount Elastic Center	211
18.8 Conclusion	211
References	212
19 Experimental Identification and Simulation of Rotor Damping	213
19.1 Introduction	213
19.2 The Two-Disc Rotor as a Test Structure	213
19.3 Layout of the Generic Joint Experiment	214
19.4 Determination of Isolated Joint's Parameters	215
19.5 Two-Disc Rotor Measurements	218
19.6 FE-Modeling	219
19.7 FE Simulation	220
19.8 Summary	221
References	221
20 An Approach to Identification and Simulation of the Nonlinear Dynamics of Anti-Vibration Mounts	223
20.1 Introduction	223
20.1.1 Nonlinear Identification Method Using Transmissibility Data	224
20.2 Application to Anti Vibration Mounts: Measurements and Results	225
20.2.1 Stepped-Sine Excitation	225
20.2.2 Nonlinear Identification	227
20.3 Numerical Simulations	228
20.3.1 Multibody Simulation	228
20.3.2 Transmissibility Computation and Method Validation	229
20.4 Conclusions	231
References	231
21 Test Method Development for Nonlinear Damping Extraction of Dovetail Joints	232
21.1 Introduction	232
21.2 The Test Rigs	233
21.3 Test Rig Support and Clamping	233
21.4 Excitation System	235
21.5 Influence of Amplitude Control	238
21.6 Discussion	239
21.7 Conclusion	240
References	240
22 Microslip Joint Damping Prediction Using Thin-Layer Elements	241
22.1 Introduction	241
22.2 Experimental Joint Parameter Extraction	242
22.3 FE Simulation	242
22.4 Differentiation Between Micro- and Macroslip	244
22.5 Conclusion	246
References	246
23 Variability and Repeatability of Jointed Structures with Frictional Interfaces	247
23.1 Introduction	247
23.2 Frequency Based Substructuring	248
23.3 Augmentation by Discontinuous Basis Functions	248
23.4 Experimental System	249
23.5 Model Comparison	252
23.6 Conclusions	253
References	254
24 Evaluation of North American Vibration Standards for Mass-Timber Floors	255
24.1 Introduction	255
24.2 Vibration Standards	256
24.2.1 AISC DG11, Chap. 4: Design for Walking Excitation	256
24.2.2 AISC DG11, Chap. 6: Design for Sensitive Equipment	257
24.2.3 CLT DH, Chap. 7: Vibration	257
24.3 Floor Stiffness	258
24.4 Scope of Study	258
24.5 Results	258
24.5.1 AISC DG11, Chap. 4: Design for Walking Excitation	258
24.5.2 AISC DG11, Chap. 6: Design for Sensitive Equipment	259
24.5.3 CLT DH, Chap. 7: Vibration	259
24.6 Conclusions	260
References	261
25 Improving Model Predictions Through Partitioned Analysis: A Combined Experimental and Numerical Analysis	262
25.1 Introduction	262
25.2 Case Study	264
25.2.1 Structure	264
25.2.2 Experimental Campaign	265
25.2.2.1 Static Testing	265
25.2.2.2 Modal Testing	265
25.3 Model A: Linear Finite Element Model with Rigid Connections	266
25.4 Linear Finite Element Model with Semi-Rigid Connections (Coupled Models)	267
25.4.1 Sensitivity Analysis	267
25.4.2 Connection Model Development	268
25.4.3 Test Analysis Correlation of Connection Models	269
25.4.4 Coupling of Frame and Connection Models	270
25.5 Results and Discussion	271
25.6 Conclusion	272
References	272
26 Model Reduction and Lumped Models for Jointed Structures	274
26.1 Introduction	274
26.2 Technical Aspects	275
26.2.1 ``Modal'' Approaches	275
26.2.2 Principal Joint Strains Basis	275
26.2.3 How to Build the Macro-models Associated with the PJSB	276
26.3 Examples	277
26.3.1 Size of the PJSB Methods	277
26.3.2 Accuracy of the PJSB Methods	277
26.4 Conclusions	278
References	280
27 A Complex Power Approach to Characterise Joints in Experimental Dynamic Substructuring	281
27.1 Introduction	282
27.2 Interface Coupling in the Framework of DS	282
27.2.1 Rigid Connection	283
In Terms of System Matrices	283
In Terms of Receptance	283
27.2.2 Compliant Interface	284
In Terms of System Matrices	284
In Terms of Receptance	284
27.3 Complex Power	286
27.3.1 Excitation Power	286
In Terms of System Matrices	286
In Terms of Receptance	286
27.3.2 Interface Power	287
27.4 Test Case	289
27.4.1 Classical Rigid Interface Connection Results	290
27.4.2 Compliant Interface Connection Results	291
Estimation of Interface Damping Based on Complex Power	291
27.5 Conclusions	293
27.6 Outlook	294
References	295
28 Prediction of Dynamics of Modified Machine Tool by Experimental Substructuring	297
28.1 Introduction	297
28.2 Analytical Model of Slide	298
28.3 Experimental Model of Frame	301
28.4 Frequency Based Substructuring with Joints	302
28.5 Coupling Results	302
28.6 Conclusion	304
References	304
29 Static Torsional Stiffness from Dynamic Measurements Using Impedance Modeling Technique	306
29.1 Introduction	307
29.2 Impedance Modeling Method	307
29.2.1 Theory	307
29.2.2 Dynamic Stiffness Method	308
29.2.3 Compliance Method	308
29.2.4 Hybrid Impedance Modeling	309
29.3 Experimental Validation	310
29.3.1 Model Calibration and Validation	311
29.3.2 Estimation of Static Torsional Stiffness Analytically	311
29.3.3 Stiffness Estimation from Impedance Modeling	311
29.3.3.1 Rigid Body Modes	312
29.3.3.2 Measurement Noise Issue	313
29.3.3.3 Parameter Estimation	313
29.4 Conclusions	313
References	314
30 Full Field Dynamic Strain on Wind Turbine Blade Using Digital Image Correlation Techniques and Limited Sets of Measured Data from Photogrammetric Targets	316
30.1 Introduction	316
30.2 Theoretical Background	318
30.2.1 Digital Image Correlation and Dynamic Photogrammetry	318
30.2.2 Model Reduction and Modal Expansion	318
30.3 Test Structure and Measured Displacement/Strain Comparisons	320
30.3.1 Test Article Description: Model and Dynamic Characteristics	320
30.3.2 Strain Gage Vs. DIC Strain Comparison: Static Testing	321
30.3.3 Strain Gage Vs. DIC Strain Comparison: Dynamic Testing—Pluck and Sine Test	322
30.3.4 Strain Gage Vs. Full Field Expansion: Dynamic Testing	323
30.4 Conclusion	325
References	327
31 Comparison of Multiple Mass Property Estimation Techniques on SWiFT Vestas V27 Wind Turbine Nacelles and Hubs	328
31.1 Introduction	328
31.2 Review of Mass Inertia Matrix	329
31.3 Mass-Line Approach	329
31.4 Rigid Body Modal Parameter Estimation Approach	329
31.5 Test Articles	330
31.6 Data Collection and Signal Processing	330
31.7 Test Results	331
31.8 Summary	335
References	335
32 Overview of the Dynamic Characterization at the DOE/SNL SWiFT Wind Facility	336
32.1 Overview of Facility	336
32.2 Turbine Characterization	337
32.3 Model Updating and Correlation	337
32.4 Summary	341
References	341
33 Artificial and Natural Excitation Testing of SWiFT Vestas V27 Wind Turbines	342
33.1 Introduction	342
33.2 Test Article and Data Collection	343
33.3 Test Results	344
33.4 Summary	348
References	352
34 Effects of Boundary Conditions on the Structural Dynamics of Wind Turbine Blades—Part 1: Flapwise Modes	353
34.1 Introduction	353
34.2 Theoretical Background	354
34.2.1 Modal Assurance Criterion	354
34.2.2 Mode Contribution Identification	355
34.3 Model Description and Cases Studied	355
34.3.1 Case 1: Modeling a 3D Wind Turbine Blade Using Beam Elements	355
34.3.2 Case 2: Developing the Turbine Model and Extracting Modes of the Turbine in a Pseudo-Fixed Configuration	357
34.3.3 Case 3: Comparing the Effects of Translational and Rotational Stiffness of the Support on the Modes of the Turbine	358
34.3.4 Case 4: Investigating the Effects of Rotational Stiffness of the Support on Flapwise Modes	359
34.3.5 Case 5: Assembling the Turbine to a Tower	360
34.3.6 Case 6: Investigating the Effects of Assembling the Turbine to a Tower	360
34.3.7 Case 7: Extracting Mode Contribution Matrix of the Wind Turbine Assembly	362
34.3.8 Case 8: Correlating the Cantilevered Single Blade to the Blades of an Assembled Wind Turbine and Perturbing the Elastic Modulus	363
34.4 Observations	364
34.5 Conclusion	365
References	365
35 Effects of Boundary Conditions on the Structural Dynamics of Wind Turbine Blades. Part 2: Edgewise Modes	367
35.1 Introduction	367
35.2 Model Description and Cases Studied	368
35.2.1 Case 1: Modeling a 3D Wind Turbine Blade Using Beam Elements	369
35.2.2 Case 2: Developing the Turbine Model and Extracting Modes of the Turbine in a Pseudo-Fixed Configuration	369
35.2.3 Case 3: Comparing the Effects of Translational and Rotational Stiffness of the Support on the Modes of the Turbine	370
35.2.4 Case 4: Investigating the Effects of Rotational Stiffness of the Support on Edgewise Modes	371
35.2.5 Case 5: Assembling the Turbine to a Tower	371
35.2.6 Case 6: Investigating the Effects of Assembling the Turbine to a Tower	373
35.2.7 Case 7: Extracting Mode Contribution Matrix of the Wind Turbine Assembly	374
35.2.8 Case 8: Correlating the Cantilevered Single Blade to the Blades of an Assembled Wind Turbine and Perturbing the Elastic Modulus	375
35.3 Observations on Edgewise Modes and Comparisons of Flapwise and Edgewise Modes	376
35.4 Conclusion	376
References	377
36 Modal Testing and Model Validation Issues of SWiFT Turbine Tests	379
36.1 Introduction	379
36.2 Test Article: Wind Turbine Blades	380
36.3 Test Results: Wind Turbine Blades	381
36.4 Test Article: Wind Turbine Towers	382
36.5 Test Results: Wind Turbine Towers	384
36.6 Summary	385
References	386
37 Development of Simplified Models for Wind Turbine Blades with Application to NREL 5 MW Offshore Research Wind Turbine	387
37.1 Introduction	387
37.2 Development of FE Models for NREL 5 MW Wind Turbine Blade	388
37.2.1 Baseline Model	388
37.2.2 Nominal Beam Model	389
37.3 FE Model Updating of Beam Model	389
37.3.1 Problem Statement	389
37.3.2 Parameter Estimation	390
37.3.3 Parameterization of the Beam Model	391
37.4 Model Reduction of Baseline Model	391
37.4.1 Model Reduction Problem	391
37.4.2 Modal Truncation	392
37.4.3 Improved Modal Truncation Algorithm	393
37.5 Results	393
37.5.1 Model Updating of the Beam Model	394
37.5.2 Model Reduction of Rotor Blade Models	397
37.6 Conclusion	398
References	400
38 A Wiki for Sharing Substructuring Methods, Measurements and Information	401
38.1 Introduction	401
38.1.1 Wiki Organization	402
38.2 Wiki Contents	404
38.2.1 Contributor Pages	404
38.2.2 Models	404
38.2.3 Experiments	404
38.2.4 Bibliography	405
38.2.5 User Pages	407
38.3 User Basics	407
38.3.1 Login or New User Set-Up	408
38.3.2 Editing an Existing Page	408
38.3.3 Create a New Page	408
38.3.4 Categories	408
38.3.5 Help and Support	409
38.4 Conclusion	409
39 Novel Parametric Reduced Order Model for Aeroengine Blade Dynamics	410
39.1 Introduction	411
39.2 Blade Reference and Modal Analysis	411
39.3 Simplified Model Concepts	412
39.4 Beam Framework Construction	412
39.5 Initial Value Determination	416
39.5.1 Step One: Expanding Mode Shape	416
39.5.2 Step Two: Deriving Structure Identification Equations	417
39.5.3 Step Three: Sort Out Ill-Condition Problems and Solve the Equations	417
39.6 Optimization Process	418
39.7 Main Results and Discussion	419
39.8 Conclusion	420
References	421
40 Practical Seismic FSSI Analysis of Multiply-Supported Secondary Tanks System	423
40.1 Introduction	423
40.2 Theoretical Background	424
40.2.1 Dynamic Pressure for Fluid Tanks	424
40.2.2 Frequency Domain Analysis Method	425
40.3 Earthquake Analysis for Fluid Tanks in Nuclear Power Plant	426
40.3.1 Simple Analysis Method	426
40.3.2 Proposed Seismic Analysis Method Using Static Analysis	426
40.3.3 Proposed Seismic Analysis Method Using Frequency Domain Analysis	427
40.4 Conclusion	429
References	429
41 DEIM for the Efficient Computation of Contact Interface Stresses	430
41.1 Introduction	430
41.2 Problem Formulation	431
41.3 Discretization	431
41.4 Model Order Reduction	433
41.5 Interface Stress Computation	434
41.5.1 POD	434
41.5.2 Stress Interpolation	434
41.5.3 DEIM	435
41.6 Numerical Example	435
41.6.1 Model Description	435
41.6.2 Reference Solution	436
41.6.3 Results	438
41.7 Conclusion	439
References	440
42 Amplitude Dependency on Dynamic Properties of a Rubber Mount	441
42.1 Introduction	441
42.2 Mathematical Model	442
42.3 Computer Implementation	444
42.4 Experimental Characterization	444
42.5 Results	446
42.6 Conclusions	448
References	448
43 Model Order Reduction for Geometric Nonlinear Structures with Variable State-Dependent Basis	449
43.1 Introduction	449
43.2 Projection Methods	450
43.3 Static Condensation Method	450
43.4 Projection Method with Variable Basis	451
43.5 Numerical Results	453
43.6 Conclusions	454
References	455
44 Stochastic Iwan-Type Model of a Bolted Joint: Formulation and Identification	457
44.1 Introduction	457
44.2 Sandia Bolted Joint Data	457
44.3 Iwan Models	458
44.4 Iwan-Type Modeling of the Sandia Joint Data: Strategy	460
44.5 Iwan-Type Modeling of the Sandia Joint Data: Detailed Uncertain Modeling	462
44.6 Stochastic Parameter Identification and Uncertainty Bands	464
44.7 Summary	465
References	466

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