Dynamics Substructures, Volume 4

Preface	6
Contents	7
1 Using Laser Vibrometry for Precise FRF Measurements in Experimental Substructuring	9
1.1 Introduction	9
1.2 Experimental Dynamic Substructuring	10
1.2.1 Frequency Based Substructuring	10
1.2.2 Virtual Point Transformation	11
1.2.2.1 Virtual Point Displacements	12
1.2.2.2 Virtual Point Forces	13
1.3 Laser Technology	14
1.4 Measurements	15
1.4.1 Measurement Setup	15
1.4.2 Virtual Point Reduction	16
1.4.3 Coupling Results	16
1.5 Conclusions	19
References	19
2 A Priori Interface Reduction for Substructuring of Multistage Bladed Disks	20
Nomenclature	20
2.1 Introduction	21
2.2 Craig-Bampton Method and Interface Reduction	21
2.2.1 Craig-Bampton Method	21
2.2.2 Craig-Bampton Method with Interface Reduction	22
2.3 Reduced Models of Multistage Bladed Disks	22
2.3.1 Single Stage Bladed Disks	23
2.3.2 Multistage Bladed Disks	23
2.4 Proposed Model Order Reduction Method	23
2.5 Application to a Two Stage Academic Rotor	24
2.6 Conclusions	27
References	27
3 Using Hybrid Modal Substructuring with a Complex Transmission Simulator to Model an Electrodynamic Shaker	29
3.1 Introduction	29
3.2 Theory	30
3.2.1 Dynamic Substructuring	30
3.2.2 Transmission Simulator Method	30
3.2.3 Mathematical Basis	31
3.3 Subsystems	32
3.3.1 The Transmission Simulator	32
3.3.2 Experimental Subsystem	32
3.3.3 Analytical Subsystem	33
3.4 Finite Element Modeling	33
3.5 Experimental Setup	35
3.6 Substructuring Prediction	38
3.7 Conclusion	39
References	40
4 Hybrid Substructure Assembly Techniques for Efficient and Robust Optimization of Additional Structures in Late Phase NVH Design: A Comparison	41
4.1 Related Work and Outline	41
4.2 Theoretical Background	42
4.2.1 Identification Methods	42
4.2.1.1 Non-parametric Identification of Frequency Response Functions	42
4.2.1.2 State-Space Identification	43
4.2.2 Hybrid Substructuring—Coupling Methods	44
4.3 Test Scenarios	45
4.3.1 Testing Procedure	45
4.3.2 Test Structures	45
4.4 Test Results	46
4.4.1 Accuracy	46
4.4.1.1 Two Mass Oscillator	46
4.4.1.2 Acoustic Testbench	47
4.4.2 Efficiency	49
4.5 Conclusion and Outlook	50
References	50
5 Workpiece Coupling in Machine Tools Using Experimental-Analytical Dynamic Substructuring	52
5.1 Introduction	52
5.2 Frequency Domain Based Workpiece Coupling	53
5.2.1 Proposed Method	53
5.2.2 Mathematical Background and Formulation	54
5.3 Sensitivity Analysis	55
5.4 Experimental Validation	57
5.4.1 Measurement Setup and Workpiece Model Validation	57
5.4.2 Measurement of Response Model Including Rotational Compliances	58
5.5 Variations of Coupling Calculations and Corresponding Results	59
5.6 Conclusions	60
References	61
6 Mechanical Characterization and Numerical Modeling of High Density Polyethylene Pipes	62
6.1 Introduction	62
6.2 Methods	63
6.3 Experiments	64
6.4 Numerical Modeling	65
6.5 Results and Discussion	66
6.6 Conclusions	69
Appendix	69
References	70
7 Study on Dynamic Stiffness Characteristic of Primary Suspension for High-Speed EMU	72
7.1 Instruction	72
7.2 Analysis Model of Axle-Box Suspension	72
7.3 Study on the Dynamic Stiffness Test Model	73
7.4 Test Method and Solving Method	74
7.5 Test Analysis	74
7.6 Conclusion	76
References	76
8 Test-Based Modeling, Source Characterization and Dynamic Substructuring Techniques Applied on a Modular Industrial Demonstrator	77
8.1 Introduction	77
8.2 Methodology	78
8.2.1 Virtual Points	78
8.2.2 Dynamic Substructuring	79
8.2.3 Source Characterization and TPA Using Blocked Forces	79
8.3 Application	79
8.4 Discussion	80
References	80
9 Development of a Low Cost Automatic Modal Hammer for Applications in Substructuring	81
9.1 Introduction	81
9.1.1 Frequency Based Substructuring	81
9.1.2 Motivation for an Automated FRF Measurement	82
9.2 Existing Technology	82
9.3 AMimpact	84
9.3.1 Description of the System	84
9.3.2 Description of the Parameters	85
9.3.3 Dynamics Model of AMimpact	85
9.4 Simulation of AMimpact	86
9.5 Results on Frequency Based Substructuring	87
9.6 Conclusion	89
References	90
10 Using SEMM to Identify the Joint Dynamics in Multiple Degrees of Freedom Without Measuring Interfaces	91
10.1 Introduction	91
10.1.1 Outline of the Paper	92
10.2 The Joint Identification Method	92
10.2.1 Frequency Based Substructuring: Coupling and Decoupling with a Weak-Formulated Joint	93
10.2.1.1 Weakening in the Interface: Adding Joint Dynamics	94
10.2.1.2 Decoupling the Components to Obtain the Joint	95
10.2.2 System Equivalent Model Mixing	95
10.2.3 The Optimisation Scheme	98
10.3 A Numerical Study	99
10.4 Discussion	102
10.5 Conclusion	102
References	103
11 Overview of Free Interface Substructuring Approaches for Systems with Arbitrary Viscous Damping in Dynamic Substructuring	104
11.1 Introduction	104
11.2 Governing Equations	105
11.2.1 Undamped and Classically Damped Systems	105
11.2.2 Nonclassically Damped Systems	106
11.3 Literature Review of Free Interface Substructuring Approaches for Viscously Damped Systems	107
11.3.1 Craig and Ni's Method Craig1989	108
11.3.1.1 Reduction Basis	108
11.3.1.2 Assembly Procedure (Elimination of Interface DOFs)	111
11.3.2 Liu and Zheng's Method Liu2008	112
11.3.2.1 Reduction Basis	112
11.3.2.2 Assembly Procedure (Elimination of Interface DOFs)	113
11.3.3 De Kraker and van Campen's Method DeKraker1996	114
11.3.3.1 Reduction Basis	114
11.3.3.2 Assembly Procedure (Primal Assembly)	115
11.4 Improvements of Free Interface Substructuring Approaches	116
11.4.1 Third and Higher-Order Reduction Interface Flexibility Representation	116
11.4.2 Combination of Liu/Zheng's Reduction Basis and Primal Assembly Procedure	117
11.5 Numerical Applications	118
11.5.1 Beam Structure with Two Localized Dampers	118
11.5.2 Damped Free-Free Beam Model	122
11.5.3 Damped Beam Model with Four Substructures and Localized Dampers	128
11.6 Conclusions	133
References	133
12 Model Updating of Fluid-Structure Interaction Effects on Piping System	135
12.1 Introduction	135
12.2 Background	135
12.3 Analysis	136
12.3.1 Test Rig and Experimentation Setup	136
12.3.2 Numerical Simulation	136
12.3.2.1 Acoustic Structural FEA	136
12.3.2.2 Model	137
12.3.2.3 Results	138
12.4 Conclusion	140
References	141
13 Vehicle Driveline Benchmarking to Support Predictive CAE Modeling Development	142
13.1 Introduction	142
13.2 Background	143
13.3 Analysis	144
13.4 Conclusion	148
References	149
14 A Proposal of Dynamic Behaviour Design Based on Mode Shape Tracing: Numerical Application to a Motorbike Frame	150
14.1 Introduction	150
14.2 Mode Shapes Tracing via Weighted Mode Shapes	151
14.3 Motorcycle Chassis Under Engine Excitation	153
14.4 Conclusions	158
References	159
15 Rapid Seismic Risk Assessment of Structures with Gaussian Process Regression	160
15.1 Introduction	160
15.2 Gaussian Process Regression	161
15.3 Case Study Results and Discussion	162
15.3.1 Model Description	162
15.3.2 Prediction Objective	162
15.3.3 Results	163
15.4 Conclusion	166
References	166
16 Modeling Rail-Vehicle Coupled Dynamics by a Time-Varying Substructuring Scheme	167
16.1 Introduction	167
16.2 Description of the Mechanical System	167
16.2.1 Rail Line Model	168
16.2.2 Moving Wheel Model	169
16.2.3 Substructure Assemblage	169
16.2.4 Modeling Wheel Defects	170
16.3 Numerical Example	170
16.4 Conclusion	171
References	171
17 Planning of a Black-Box Benchmark Structure for Dynamic Substructuring	172
17.1 Research Strategy	172
17.2 Challenge Schedule	173
17.3 Design Considerations	173
17.4 Closing Remarks	174
References	174
18 Study on the Technology of Reliable Life Prediction of Plate Heat Exchanger for Ship	175
18.1 Introduction	175
18.2 Establish the Reliable Life Prediction Model with Information of Similar Products	176
18.2.1 Basic Hypothesis	176
18.2.2 The Principles and Approaches of the Assessment on Reliable Life	176
18.2.3 Calculation of Conversion Ratio of Similar Products Based on the Fuzzy Degree of Nearness	177
18.3 Reliability Lifetime Prediction for Plate Heat Exchanger	178
18.3.1 Analysis on Similar Factors of Plate Heat Exchanger	178
18.3.2 Usual Failure Mode and Sensitive Stresses on Plate Heat Exchanger	178
18.3.3 Calculating Conversion Ratio by Severity of Working Environment and Own Factor	179
18.4 Reliability Life Prediction of Plate Heat Exchanger Based on Conversion Factor	179
18.5 Result and Discussion	180
References	180
19 Real-Time Hybrid Substructuring Results of the Mars Pathfinder Parachute Deployment	181
19.1 Introduction	181
19.2 RTHS Test Equipment	182
19.3 Results	183
19.4 Conclusions	184
References	184

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