Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8

Preface	5
Contents	6
1 Strategies for Testing Large Aerospace Structures with 3D SLDV	8
1.1 Introduction	8
1.2 Challenges Associated with Large Aerospace Test Articles	9
1.3 Case Study Tests	9
1.3.1 Conical Structure Modal Test	9
1.3.1.1 Data Acquisition Setup	10
1.3.1.2 Laser Alignment	11
1.3.1.3 Data Analysis	12
1.3.1.4 Lessons Learned from the Conical Test Article	12
1.3.2 Empty Bomb Case Modal Test	15
1.3.2.1 Data Acquisition Setup	15
1.3.2.2 Laser Alignment	15
1.3.2.3 Data Analysis	17
1.4 Lessons Learned and Lingering Deficiencies	17
1.5 Conclusions	19
References	19
2 Modal Model Validation Using 3D SLDV, Geometry Scanning and FEM of a Multi-Purpose Drone Propeller Blade	20
Abbreviations	20
2.1 Introduction and Motivation	20
2.2 Materials and Methods: Experimental Modal Analysis	22
2.3 Materials and Methods: Geometry Scanning, Reverse Engineering and FE Simulation	24
2.4 Results and Discussion	26
2.5 Conclusions and Further Work	27
References	29
3 Effect of Dry Friction Damping on the Dynamic Response of Helicopter Tail Shaft	30
3.1 Introduction	30
3.2 Mathematical Model of the System	31
3.3 Solution Methodology	31
3.4 Harmonic Balance Method	32
3.5 Case Studies	34
3.6 Conclusion	37
References	37
4 Nonlinear Dynamic Analysis of a Spiral Bevel Geared System	38
Nomenclature	38
Subscripts	39
Superscripts	39
4.1 Introduction	39
4.2 Dynamic Model Formulation	40
4.2.1 Physical System and Dynamic Model	40
4.2.2 Solution Method	42
4.2.2.1 Multi-Term Harmonic Balance Method with DFT	42
4.3 Results and Discussion	43
4.4 Conclusion	46
References	47
5 Estimating Material Wavespeed Using the Wavenumber Transform of RectangularPlate Mode Shapes	48
5.1 Introduction	48
5.2 Methodologies	48
5.2.1 Wavenumber Transform Theory	48
5.2.2 Discrete Wavenumber Transform	50
5.2.3 Determination of Mode Shapes	51
5.2.4 Computation of Wavespeed	51
5.3 Results: Thin, Aluminum Plate	51
5.4 Conclusions	53
References	53
6 In-Operation Wind Turbine Modal Analysis via LPV-VAR Modeling	54
6.1 Introduction	54
6.2 Methods	55
6.2.1 The Linear Parameter Varying Vector AR model	55
6.2.1.1 Estimation of the Parameter Matrix and Innovations Covariance Matrix	56
6.2.2 Covariance Matrix of the Parameter Estimates	57
6.2.3 Model Based Analysis	57
6.2.4 Extraction of Linear Parameter Varying Mode Shapes	59
6.3 Application Example	59
6.3.1 Simulated Operating Wind Turbine Vibration	59
6.3.2 Identification of the LPV-VAR Model	60
6.3.3 Model Based Analysis	62
6.4 Conclusion	62
References	64
7 Structural Damage Identification Using Free Response Measured by a Continuously Scanning Laser Doppler Vibrometer System	65
7.1 Introduction	65
7.2 Methodology	66
7.2.1 Free Response of a Damped Beam Structure	66
7.2.2 FRS	67
7.2.3 Demodulation Method for FRSs	68
7.2.4 FRDI	69
7.3 Numerical Investigation	70
7.3.1 FRSs from Analytical and FE Models	70
7.3.2 Damage Identification Using FRDIs	71
7.4 Conclusion	71
References	76
8 Mitigation of Structural-Acoustic Mode Coupling in a Modal Test of a Hollow Structure	77
Abbreviations	77
8.1 Introduction	77
8.2 Description of Hardware and Test Setup	78
8.3 Modal Hammer Test Results Indicate Acoustic Coupling	79
8.3.1 Initial Modal Test Results	79
8.3.2 Coupled Structural-Acoustic Finite Element Model	79
8.3.2.1 Structural Model	79
8.3.2.2 Acoustic Model	79
8.3.2.3 Coupled Finite Element Model	81
8.3.3 Initial Decoupling Attempt	81
8.4 Coupling Effects Demonstrated with a Simple Two Degree of Freedom Model	82
8.4.1 Effects of Modal Frequency Proximity	84
8.4.2 Effect of Air Damping When Structural and Acoustic Frequencies Are In-Tune	85
8.4.3 Effect of Air Damping When Frequencies Are Well Separated	86
8.5 Experimental Study of the Effect of Added Air Damping	86
8.5.1 Decoupling Strategy 1: Non-Contact Foam Covered Rod	87
8.5.2 Decoupling Strategy 2: Foam Blocks Set Directly on Inner Wall of Cylinder	87
8.5.3 Effect of Added Absorptive Material on the (2,1) Ovaling Mode	88
8.6 Conclusions and Future Work	89
References	90
9 Applications of 3D Scanning Laser Doppler Vibrometry to an Article with Internal Features	91
9.1 Introduction	91
9.2 Test Article	92
9.2.1 Preliminary Model Predictions	92
9.3 Initial Roving Hammer Testing	92
9.3.1 Test Setup	92
9.3.2 Results	94
9.4 3D LDV Testing	94
9.4.1 Test Setup	95
9.4.2 Results	97
9.5 Comparison of Roving Hammer and LDV Results	99
9.6 Model Updating and Correlation	100
9.7 Conclusions	101
Reference	101
10 The Measurement of a Nonlinear Resonant Decay Using Continuous-Scan Laser DopplerVibrometry	102
10.1 Introduction	102
10.2 Background	103
10.2.1 High-Speed 3D-DIC Processing	103
10.2.2 CSLDV Processing	104
10.2.3 Structure of Interest	104
10.3 Results	105
10.4 Conclusions	107
References	108
11 Vibro-Acoustic Modulation of a Spinning Apparatus for Nondestructive Evaluation	110
11.1 Introduction	110
11.2 Experimental Procedures	111
11.2.1 Experimental Setup for Vibro-Acoustic Modulation	111
11.3 Analysis	113
11.3.1 Analysis Methods for VAM	114
11.4 Results	115
11.4.1 Localization Using VAM	115
11.5 Conclusions	118
References	119
12 Nonlinear Phase Separation Testing of an Experimental Wing-Engine Structure	120
References	122
13 Wind Turbine Health Monitoring: Current and Future Trends with an Active Learning Twist	123
13.1 The Past, the Present, the Laboratory and the Reality	123
13.2 Intelligent WT and the Future	124
13.3 An Active Learning Twist	124
13.4 An Illustrative Toy Example	125
13.5 Offshore Wind Farm Active Learning Approach	126
13.6 Conclusion	131
References	132
14 Nonlinear 3D Dynamic Model of an Automotive Dual Mass Flywheel	134
Nomenclature	134
14.1 Introduction	135
14.2 DMF Torsional Model	136
14.2.1 Description of Bodies, Constraints and Number of d.o.f.	136
14.2.2 Equations of Motion	137
14.3 Numerical-Experimental Comparison	140
14.3.1 Torsion Test at Standstill	140
14.3.2 Small Displacement Cycles at Different Rotating Speeds	140
14.4 DMF 3D Model	142
14.5 Analysis on the Complete Driveline Multibody Model	143
14.6 Conclusion	143
References	145
15 Investigation of Notch-Type Damage Identification by Using a Continuously Scanning Laser Doppler Vibrometer System	146
15.1 Introduction	146
15.2 Methodology	147
15.2.1 CSLDV System	147
15.2.1.1 Demodulation Method	148
15.2.2 Curvature-Based Damage Identification Method	149
15.3 Experimental Investigation of Notch-Type Damage Identification	150
15.3.1 Notch Identification Along the Whole Length of the Beam	151
15.4 Conclusion	152
References	153

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