Special Topics in Structural Dynamics, Volume 6

Preface	6
Contents	8
1 Development of Reduced Order Models to Non-modeled Regions	10
Nomenclature	10
1.1 Introduction	11
1.2 Theoretical Background	11
1.2.1 Model Reduction/Expansion Techniques	11
1.2.2 System Equivalent Reduction Expansion Process (SEREP)	13
1.2.3 Modal Assurance Criterion (MAC)	14
1.2.4 Pseudo Orthogonality Check (POC)	14
1.3 Model Description	14
1.3.1 Model 1 (Line)	15
1.3.2 Model 2 (Shell)	15
1.3.3 Model 3 (Hybrid)	15
1.3.4 Model 4 (Hybrid-Offset)	15
1.3.5 Model 5 (Hybrid-1 Node)	15
1.4 Cases Studied	16
1.4.1 Case X	16
1.4.2 Case Y	17
1.4.3 Case Z	18
1.5 Conclusion	19
References	20
2 Prediction of Forced Response Using Expansion of Perturbed Reduced Order Models with Inexact Representation of System Modes	21
Nomenclature	21
Symbols	21
Acronyms	22
2.1 Introduction	22
2.2 Theory	23
2.2.1 Equations of Motion for Multiple Degree of Freedom System	23
2.2.2 Structural Dynamic Modification	24
2.2.3 General Reduction/Expansion Methodology and Model Updating	25
2.2.3.1 System Equivalent Reduction Expansion Process (SEREP)	25
2.2.3.2 KM_AMI Reduction	25
2.2.4 System Forced Response Analysis	26
2.2.5 Time Response Correlation Tools	26
2.2.5.1 Modal Assurance Criterion (MAC)	26
2.2.5.2 Time Response Assurance Criterion (TRAC)	27
2.3 Model Description	27
2.4 Cases Studied	27
2.4.1 Case A-1: Reference Model	30
2.4.2 Case A-2: Guyan Reduced Order Models	30
2.4.2.1 Case A-2.1	30
2.4.2.2 Case A-2.2	31
2.4.3 Case A-3: SEREP Reduced Order Models	32
2.4.3.1 Case A-3.1	32
2.4.3.2 Case A-3.2	32
2.4.4 Case A-4: KM_AMI Model Improvement from Guyan Reduced Order Models	33
2.4.4.1 Case A-4.1	34
2.4.4.2 Case A-4.2	34
2.4.5 Overview of Case B	35
2.4.6 Case B-1: Modified/Perturbed Reference Model (Imperfect FEM Representation of Truth Model)	35
2.4.7 Case B-2: Reduced Order Models of Reference Beam (Unmodified)	36
2.4.7.1 Case B-2.1	37
2.4.7.2 Case B-2.2	38
2.4.7.3 Case B-2.3	40
2.5 Observations	41
2.6 Conclusions	41
References	42
3 Estimation of Rotational Frequency Response Functions	43
3.1 Introduction	43
3.2 Theoretical Development	44
3.2.1 Data Expansion Techniques	44
3.2.1.1 System Equivalent Reduction Expansion Process	45
3.2.1.2 Kidder's Method	45
3.2.1.3 Modified Kidder's Method	45
3.2.2 FRF Expansion Techniques	46
3.2.2.1 FRF Expansion Using SEREP	47
3.2.2.2 FRF Expansion Using the Modified Kidder's Method	47
3.3 Numerical Simulations	48
3.4 Results And Discussion	50
3.5 Conclusions	55
References	56
4 Estimation of Spatial Distribution of Disturbances	57
4.1 Introduction	57
4.2 The Kalman Filter	58
4.3 Innovations Correlations Approach	58
4.4 Numerical Experiment: Five-DOF Spring Mass System	60
4.5 Conclusions	62
References	62
5 Body Wise Time Integration of Multi Body Dynamic Systems	63
Nomenclature	63
5.1 Introduction	64
5.2 Theory	64
5.2.1 Body Iteration	65
5.2.2 Constraint Update	66
5.3 Numerical Time Integration	68
5.4 Conclusion	69
References	69
6 Structural Dynamic Modeling: Tales of Sin and Redemption	70
6.1 Introduction	70
6.2 Nomenclature	71
6.3 Structural Dynamics Modeling: The Present State-of-the-Art	71
6.3.1 Proportional Damping Formulations	72
6.3.2 Assembly of Structural Dynamic Models from Discrete Components	72
6.3.3 Interaction of Structures with Fluid Media	73
6.4 Damping in Structural Assemblies	73
6.4.1 Evidence of Displacement Proportional Structural Damping	74
6.4.2 Viscoelastic Material Behavior and Structural Joint Models	74
6.4.3 A Fresh Look at Structural Damping	77
6.5 Interface Flexibility in Structural Assemblies-A Retrospective	77
6.6 Conclusions	78
References	79
7 Muscle Property Identification During Joint Motion Using the NL-LTP Method	81
7.1 Introduction	81
7.2 Model and Simulation	82
7.3 Results	85
7.4 Discussion	87
7.5 Conclusions	88
Appendix	88
References	89
8 On the Detectability of Femoral Neck Fractures with Vibration Measurements	90
8.1 Introduction	90
8.2 Patients and Methods	91
8.3 Ethics	92
8.4 Results and Discussion	92
8.5 Reproducibility of FRFs	93
References	94
9 Static Calibration of Microelectromechanical Systems (MEMS) Accelerometers for In-Situ Wind Turbine Blade Condition Monitoring	95
9.1 Introduction	95
9.2 MEMS Accelerometers and Positioning	96
9.3 Static Calibration	97
9.3.1 Methodology: Least Square Approximation	98
9.3.2 Results	100
9.4 Conclusions	101
References	101
10 Predicting Full-Field Strain on a Wind Turbine for Arbitrary Excitation Using Displacements of Optical Targets Measured with Photogrammetry	103
Nomenclature	103
10.1 Introduction	104
10.2 Theory	105
10.2.1 Expansion	105
10.2.2 Correlation Tools	106
10.3 Test Setup	107
10.4 Modeling and Data Processing	107
10.5 Cases Studied	109
10.5.1 Sine Dwell Excitation	109
10.5.2 Pluck Test	109
10.5.3 Random Impact Excitations	109
10.5.4 Random Excitation with a Mechanical Shaker	110
10.6 Observations	111
10.7 Conclusions	113
References	117
11 Predicting the Vibration Response in Subcomponent Testing of Wind Turbine Blades	119
11.1 Introduction	119
11.2 Governing Equations	120
11.2.1 Vibration of Specially Orthotropic Laminated Plate	120
11.3 Complete Similarity	121
11.4 Partial Similarity	122
11.4.1 Distortion in Aspect Ratio	123
11.4.2 Distortion in Ply Stack Up	123
11.5 Discussion	124
11.6 Conclusion	126
References	127
12 Linear Modal Analysis of a Horizontal-Axis Wind Turbine Blade	128
12.1 Introduction	128
12.2 Model Definition	129
12.3 Equations of Motion	130
12.4 Case Studies	130
12.4.1 A Hollow Rectangular Beam with a Structural Twist	130
12.4.2 NREL's 5 MW Turbine Blade	132
12.5 Conclusions	133
References	133
13 Reduced-Order Modeling of Turbine Bladed Discs by 1D Elements	135
13.1 Introduction	135
13.2 1-D Modelling of a Turbine Blade	136
13.3 Cross-Section	136
13.4 Beam Model	138
13.5 Mesh Assemblage	143
13.6 Solution	143
13.7 Validation	143
13.8 Closing Remarks	145
References	145
14 Damping Estimation for Turbine Blades Under Non-stationary Rotation Speed	146
14.1 Introduction	146
14.2 Description of the Problem	147
14.3 Effects of the Sweep Rate	147
14.4 Time-Frequency Analysis	150
14.5 Identification of Time-Variant Systems	151
14.6 Concluding Remarks	153
References	153
15 Finite Element Modeling of a 40m Space Frame Wind Turbine Tower	154
15.1 Introduction	154
15.2 Experimental Testing of the Tower	155
15.3 Modeling of the Tower	156
15.3.1 Modeling of the Filleted L-Beam	157
15.3.2 Modeling of the Bolted Joint Connections	159
15.3.2.1 Modeling of the Regular Bolted Joints	159
15.3.2.2 Modeling of the Interference-Pin Bolted Joint Connection	161
15.3.3 Simulation of L-Beams and Joints	162
15.3.3.1 Simulation of Filleted L-Beam Versus Non-filleted L-Beam	162
15.3.3.2 Simulation of Actual Tower Lay-Out Bolted Joints Versus No Bolts and All Regular Bolts	163
15.3.4 Assembling the Tower	164
15.3.5 Modeling of the Ground Surrounding the Tower	166
15.4 Conclusion	169
References	170
16 Experimental Validation of Modal Parameters in Rotating Machinery	171
16.1 Introduction	171
16.2 Experimental Modal Analysis of Rotating Systems	172
16.2.1 The Linear Speed Dependent Model	172
16.2.2 Cyclic Energy Dissipation and Stability	172
16.2.3 Modeling of Rotating Damping	173
16.3 Estimation of the Damping Matrix	173
16.3.1 Damping Matrix Estimation Methods	173
16.3.2 Limitations of the Damping Estimation Method	174
16.3.2.1 Mode Shape Errors	174
16.3.2.2 Incomplete Data and Modal Truncation	174
16.4 Extracting the Rotating Damping Effect from Measurements	174
16.4.1 The Rotating Damping Setup	174
16.4.2 Nonrotating Shaft	175
16.4.2.1 Modeling, Updating and Reducing of the Model	175
16.4.2.2 Identification of the Damping Matrix	175
16.4.3 Rotating Shaft	176
16.5 Experimental Validation	176
16.6 Conclusion	177
References	178
17 Estimation of Modal Damping for Structures with Localized Dissipation	179
17.1 Introduction	179
17.2 Energetic Method	179
17.3 Advantages and Limitations of the Energetic Method	181
17.3.1 Influence of the Mode Projection	181
17.3.2 Effects of the Localized Damping Level	184
17.3.3 Influence of Modal Density	186
17.4 Conclusion	190
References	191
18 Design of UAV for Surveillance Purposes	192
18.1 Introduction	192
18.2 Scan and Identification	193
18.3 Definition of the Path, Priority and Coming Back: The Neural Network	195
18.4 Conclusions	197
References	197
19 An Innovative Solution for Carving Ski Based on Retractile Blades	199
19.1 Introduction	199
19.2 The Prototype	200
19.3 The Field Test	202
19.3.1 The Test Track	202
19.3.2 Experimental Setup	202
19.3.3 The Experimental Results	203
19.4 Conclusion and Future Work	204
References	205

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