Rotating Machinery, Vibro-Acoustics & Laser Vibrometry, Volume 7

Preface	6
Contents	7
1 Summarizing Results for Scaling OMA Mode Shapes by the OMAH Technique	9
1.1 Introduction	9
1.2 Theory	10
1.2.1 OMAH Mode Shape Scaling	10
1.2.2 Estimating Harmonics in Noise	12
1.2.3 Guidelines for Applying OMAH	13
1.3 Discussion	14
1.4 Conclusions	15
References	16
2 Delamination Identification of Laminated Composite Plates Using a Continuously Scanning Laser Doppler Vibrometer System	17
2.1 Introduction	17
2.2 Methodology	18
2.2.1 Damage Identification Using Curvature Vibration Shapes	18
2.2.2 Demodulation Method	19
2.2.3 Polynomial-Based Damage Identification	20
2.2.4 Wavelet-Based Damage Identification	21
2.3 Experimental Investigation	22
2.4 Conclusions	24
References	26
3 Rapid and Dense 3D Vibration Measurement by Three Continuously Scanning Laser DopplerVibrometers	27
3.1 Introduction	27
3.2 Methodology	28
3.2.1 Geometrical Model of a CSLDV	28
3.2.2 Constant-Speed Scan for the Top CSLDV	29
3.3 Experimental Investigation	31
3.3.1 3D ODSs in the MCS by the 3D-CSLDV System	31
3.3.2 Comparison with Step Scanning	31
3.4 Conclusions	33
References	36
4 Modal Control of Magnetic Suspended Rotors	38
4.1 Introduction	38
4.2 Modal Robust Control	39
4.3 Model and Numerical Results	40
4.4 Conclusion	47
References	47
5 On the Implementation of Metastructures in Rotordynamics	49
5.1 Introduction	49
5.1.1 Metastructure Definition	50
5.1.2 Element Tuning	52
5.1.3 Dynamic Response Estimation	53
5.1.4 Geometry Optimization	54
5.2 Conclusions	55
References	56
6 Analysis of the Dynamic Response of Coupled Coaxial Rotors	58
Nomenclature	58
6.1 Introduction	59
6.2 Theory	59
6.2.1 Model of Interest	59
6.2.2 Equations of Motion	60
6.2.3 Natural Frequencies and Mode Shapes	61
6.2.4 Critical Speeds	61
6.2.5 Summary	61
6.3 Modal Analysis of the Baseline System	61
6.3.1 Co-rotating Rotors	62
6.3.2 Counter-rotating Rotors	63
6.3.3 Summary	65
6.4 Parameter Study	65
6.4.1 Inter-shaft Bearing Stiffness	66
6.4.1.1 Natural Frequencies and Mode Shapes	66
6.4.1.2 Critical Speeds	67
6.4.2 Rotor Speed Ratio	68
6.4.2.1 Natural Frequencies and Mode Shapes	68
6.4.2.2 Critical Speeds	69
6.4.3 Summary	69
6.5 Conclusions	70
References	70
7 Operational Modal Analysis of Rotating Machinery	71
7.1 Introduction	71
7.2 Framework for OMA with Harmonic Disturbances	72
7.2.1 Harmonic Detection	72
7.2.2 Harmonic Reduction	73
7.2.3 Modal Parameters Computation	73
7.3 Results	74
7.4 Conclusion	78
References	78
8 Characterization of Torsional Vibrations: Torsional-Order Based Modal Analysis	80
8.1 Introduction	80
8.2 Operational Analysis Techniques	81
8.2.1 Operational Deflection Shapes	81
8.2.2 Operational Modal Analysis	82
8.2.3 Order Based Modal Analysis	82
8.2.3.1 Time Domain Sampling Based Fast Fourier Transform Order Tracking (FS)	83
8.2.3.2 Resampling Based Order Tracking (AD)	84
8.3 Torsional-Order Based Modal Analysis	85
8.3.1 Multi-orders Algorithm	86
8.4 Application Cases	87
8.4.1 Simulated Example	87
8.4.2 Experimental Case	91
8.5 Conclusions	92
References	92
9 Long-Term Automatic Tracking of the Modal Parameters of an Offshore Wind Turbine Drivetrain System in Standstill Condition	93
9.1 Introduction	93
9.2 Offshore Measurements	94
9.3 The Automatic Tracking Approach of the Drivetrain's Modal Behavior	95
9.4 Results and Discussions	97
9.5 Conclusions	99
References	100
10 Dynamic Modelling and Vibration Control of a Turbomolecular Pump with Magnetic Bearings in the Presence of Blade Flexibility	102
10.1 Introduction	102
10.2 Mechanical Model	102
10.2.1 Energetic Approach and Rayleigh-Ritz Approximation	103
10.2.2 Modal Analysis and Rayleigh Quotient Applied to Rotating Structures	105
10.3 Results and Model Updating	106
10.3.1 Experimental Modal Identification	106
10.3.2 Results at Rest: Conservative System	107
10.3.3 Spinning Results: Conservative System	108
10.4 Conclusions and Perspectives	110
References	111
11 Pushing 3D Scanning Laser Doppler Vibrometry to Capture Time Varying Dynamic Characteristics	112
11.1 Introduction	112
11.2 Test Article Description	113
11.3 Preliminary 3D SLDV Modal Survey	113
11.4 Activated Test Setup	115
11.5 Data Acquisition and Processing	116
11.6 Results	118
11.7 Technical Issues & Conclusions	121
References	122
12 Dynamic Measurements on Miniature Springs for Flaw and Damage Detection	123
12.1 Introduction	123
12.2 Spring Dynamic Testing	124
12.3 Natural Frequency Distributions	126
12.4 Flawed Spring Detection	126
12.5 Discussion	131
References	135
13 Using High-Resolution Measurements to Update Finite Element Substructure Models	136
13.1 Introduction	136
13.2 Preliminary Finite Element Model	137
13.3 Experimental Modal Test and Analysis	137
13.3.1 Laser Alignment	137
13.3.2 Blade Testing and Preliminary FEM Updating	139
13.4 Finite Element Model Updating	141
13.4.1 Berman-Nagy Approach	142
13.4.2 Analytical Model Improvement Approach	144
13.4.3 Variability Improvement of Key Inaccurate Node Groups	145
13.5 VIKING Discussion	146
13.6 Summary	147
References	147
14 Determination of Representative Offshore Wind Turbine Locations for Fatigue Load Monitoring by Means of Hierarchical Clustering	148
14.1 Introduction	148
14.2 Model and Load Assumptions	148
14.3 Clustering Procedure	149
14.4 Results	150
References	151
15 Effect of Friction-Induced Nonlinearity on OMA-Identified Dynamic Characteristics of Offshore Platform Models	152
15.1 Introduction	152
15.2 Description of the Experimental Set-Up	153
15.3 Methodology	155
15.4 Experimental Results	156
15.4.1 Linear Case	156
15.4.2 Nonlinear Case: High Intensity	157
15.4.3 Nonlinear Case: Low Intensity	158
15.5 Conclusion	160
References	160
16 Remote Damage Detection of Rotating Machinery	162
16.1 Introduction	162
16.2 Background	163
16.2.1 Motor Current Signature Analysis (MCSA)	163
16.2.2 Motor Vibrational Analysis (MVA)	164
16.2.3 Signal Processing Techniques	164
16.3 Experimental Setup	165
16.3.1 Instrumentation and Data Acquisition	165
16.3.2 General Motor Vibration Signal Acquisition	165
16.3.3 Application Environment Motor Vibration Signal Acquisition	167
16.3.4 Damaged Vibration Signal Acquisition	167
16.4 Frequency Response Function (FRF) Development and Comparison	168
16.4.1 Asynchronous Frequency Response Function (AFRF) Development	168
16.4.2 Asynchronous Frequency Response Function Validation	168
16.5 Damage Detector	168
16.5.1 Damage Detection Model	169
16.5.2 Damage Detector Formulation	169
16.6 Results and Analysis	171
16.6.1 Frequency Response Function Development and Validation Results	171
16.6.2 Damage Detection Results	173
16.7 Discussion	173
16.8 Conclusion	176
References	177
17 Experimental Demonstration of a Tunable Acoustoelastic System	178
17.1 Introduction	178
17.2 Hardware and Test Set-up	179
17.3 Identification and Measurements of Acoustoelastic Coupling	179
17.3.1 Repeatability Testing	180
17.3.2 Coupling Identification	181
17.3.3 Coupled Mode Shapes	182
17.4 Coupling Mitigation Strategies	183
17.4.1 Acoustic Modifications	184
17.4.1.1 Partition Inclusion	184
17.4.1.2 Foam Inclusion	184
17.4.1.3 Randomly Distributed Paper Towels	185
17.4.2 Structural Modifications	186
17.5 Conclusions and Future Work	187
References	188
18 Numerical Modeling of an Enclosed Cylinder	189
18.1 Introduction	189
18.2 Designing an Acoustoelastic System Using Simulation	189
18.2.1 Parameterized Finite Element Shell Models	190
18.2.2 Analytical Acoustic Modes Model	190
18.2.3 Final Design Selection	190
18.2.4 Example Test Data	191
18.3 Finite Element Simulations to Explore Changes to the Acoustoelastic System	192
18.3.1 Coupled Finite Element Fluid Mesh	192
18.3.2 Coupled Boundary Element Fluid Mesh	192
18.3.3 Simulating Changes to the Air Damping	192
18.3.4 Simulating Changes to the Air Sound Speed	192
18.3.5 Simulating Changes to the Geometry of the Air Cavity: Adding a Partition	193
18.3.6 Simulating Changes to the Structural Mass	194
18.3.7 Summary of Effects of System Changes	194
18.4 Conclusions	195
References	195
19 Exploiting Laser Doppler Vibrometry in Large Displacement Tests	196
19.1 Introduction	196
19.2 Numerical Model	197
19.3 Results	197
19.4 Estimation of Accuracy	200
19.5 Conclusions	201
References	202
20 A Rational Basis for Determining Vibration Signature of Shaft/Coupling Misalignment in Rotating Machinery	203
20.1 Introduction	203
20.2 Basic Concept	204
20.3 Experiment	206
20.4 Results	207
20.5 Conclusions	211
References	213
21 Parametric Experimental Modal Analysis of a Modern Violin Based on a Guarneri del Gesù Model	214
21.1 Introduction	214
21.2 Experimental Setup	215
21.3 Identification of Modal Properties and Configuration Comparison	218
21.4 Conclusion	222
References	224
22 Influence of the Harmonics on the Modal Behavior of Wind Turbine Drivetrains	226
Nomenclature	226
22.1 Introduction	226
22.2 Theoretical Background	227
22.2.1 Poly Least Square Complex Frequency Domain Estimator	227
22.2.2 Cepstrum Analysis for Operational Modal Analysis	228
22.3 Methodology	229
22.4 Results	230
22.5 Conclusions	232
Bibliography	233
23 The Influence of Geometrical Correlation in Modal Validation Using Automated 3D Metrology	234
Nomenclature	234
23.1 Introduction	235
23.2 Materials and Methods	236
23.3 Results and Discussion: Correlation of Modal Parameters Obtained by EMA and FEA	236
23.4 Results and Discussion: The Influence of the Geometrical Correlation	237
23.5 Conclusions	237
References	239

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