Topics in Modal Analysis, Volume 7

Preface	6
Contents	8
1 Damage Detection Using Flexibility Proportional Coordinate Modal Assurance Criterion	12
1.1 Introduction	12
1.2 Damage Sensitive Feature	13
1.2.1 Mode Shape Normalization	14
1.2.2 Damage Location	15
1.3 Damage Detection Algorithm	16
1.3.1 Training	16
1.3.2 Testing	17
1.4 Results	18
1.5 Conclusions	19
References	19
2 Automated Selection of Damage Detection Features by Genetic Programming	20
2.1 Introduction	20
2.1.1 Structural Health Monitoring	20
2.1.2 Genetic Programming	21
2.1.3 Paper Overview	21
2.2 Genetic Programming System	21
2.2.1 Solution Structure	21
2.2.2 Function and Terminal Sets	22
2.2.3 Fitness	22
2.2.4 Breeding	22
2.2.5 Genetic Programming Summary	22
2.3 Signal Detection Results	23
2.3.1 Motivation	23
2.3.2 Problem Description	23
2.3.3 Detection Results	25
2.4 Conclusion	25
References	27
3 Optimal Selection of Artificial Boundary Conditions for Model Update and Damage Detection – Part 1: Theory	28
3.1 Introduction	28
3.2 Background	29
3.3 Artificial Boundary Condition Sets	30
3.4 Identification of Natural Frequencies for an Omitted Coordinate System	30
3.5 The Updating Problem and Its Solutions	31
3.5.1 Least-Norm Versus Basic Solutions	32
3.5.2 QR Decomposition with Column Pivoting for Subset Selection	33
3.6 Simulation Model and OCS Frequencies	34
3.6.1 Generation of Artificial Boundary Condition (ABC) Sets	36
3.6.2 QR Basis Inclusion Flag	37
3.6.3 Updating Solution Performance Metrics	38
3.6.4 Simulation Results	38
3.6.5 Multiple OCS	42
3.7 Summary and Conclusions	45
References	46
4 Optimal Selection of Artificial Boundary Conditions for Model Update and Damage Detection – Part 2: Experiment	48
4.1 Introduction	48
4.2 Description of Experiment	49
4.3 Initial Mass Modeling	49
4.4 Finite Element Modeling: Localization Parameters	50
4.5 Set Definitions	50
4.6 ABC-QR Procedure	50
4.7 Measured FRF Data	52
4.8 ABC Frequency Identification: Theory	52
4.9 ABC Frequency Calculation	52
4.10 Localization Experiments	55
4.11 Conclusions and Discussion	64
References	71
5 Detection of Mass Change on a Glass Plate	72
5.1 Introduction	72
5.2 Theoretical Aspects	73
5.2.1 Mode Shape Sensitivity Equation	73
5.2.2 Bernal Projection Equation	74
5.2.3 Final System of Equations	74
5.3 Case Study: Glass Plate	75
5.3.1 Finite Element Model	75
5.3.2 Simulation Results	76
5.4 Conclusions and Future Work	77
References	77
6 Vibro-Acoustic Research on a Full-Scale Aircraft Structure	78
6.1 The A400M	78
6.2 Research and Development of Active Noise and Vibration Suppression	79
6.2.1 Active Noise Control in the Load Master Area	79
6.2.2 Tunable Vibration Absorber System	79
6.3 State of the Art of Vibro-Acoustic Test Environments	80
6.3.1 Aircraft Panel Structure (Helmut-Schmidt-University)	80
6.3.2 Wooden Mock Up for ANC Development (Helmut-Schmidt-University)	80
6.3.3 Beechcraft Starship Fuselage (BSF) and Aluminium Testbed Cylinder (ATC) at NASA Langley Research Center	82
6.3.4 UHB (Ultra High Bypass) Demonstrator MD-80	83
6.3.5 Advanced Study for Active Noise Control in Aircraft (ASANCA)	84
6.4 A400M Test Structure at Helmut-Schmidt-University	84
6.5 Prospective Future Research Activities	86
References	87
7 Control of Dynamic Mass as Boundary Condition for Testing Substructures	88
7.1 Introduction of Damped Two Mass-Spring System	88
7.2 Simulation of Damped Two Mass-Spring System	89
7.3 Introduction Flexible Beam	90
7.4 Experiment with Flexible Beam	91
7.5 Conclusion	93
References	94
8 Multi-body-Simulation of a Self Adaptive Torsional Vibration Absorber	95
8.1 Introduction	95
8.2 Design of Vibration Absorber	95
8.2.1 Multibody Model	95
8.2.2 Dynamic Influence of Absorber Mass	97
8.2.3 Dynamic Influence of Beam Length	98
8.2.4 Design Parameters	98
8.3 Power Train with Vibration Absorber	98
8.3.1 Multibody Model	99
8.3.2 System Dynamics	99
8.4 Conclusion	101
References	101
9 Combined Optimization of Actuator/Sensor Positions and Weighting Matrices for an Active Noise Reduction System	102
9.1 Introduction	102
9.2 Combined Optimization	103
9.2.1 Basic Equations	103
9.2.2 Objective Function and Optimization Parameters	103
9.2.3 Constraints and Restrictions	104
9.2.4 Implementation	104
9.3 Application to Work Station	105
9.3.1 Comparison of Optimization Results	106
9.3.2 Validation of Optimization Results	107
9.4 Conclusion and Outlook	107
References	107
10 SSDI Technique Evolution to Improve Attenuation Performances with Random Disturbances	108
10.1 Introduction	108
10.2 The Synchronized Switch Damping on Inductance Method	109
10.3 Test Case Structure and Its Model	110
10.4 Evolution of the SSDI Technique	112
10.5 Conclusion	112
References	113
11 Geometrically Nonlinear Dynamic Analysis of Piezoelectric Integrated Thin-Walled Smart Structures	115
11.1 Introduction	115
11.2 Numerical Methods	116
11.2.1 Nonlinear Strain Terms	116
11.2.2 Constitutive Equations	117
11.2.3 Dynamic Equations	117
11.2.4 Central Difference Method	117
11.3 Example Simulations	118
11.3.1 Cantilevered Beam	118
11.3.2 Fully Clamped Plate	119
11.3.3 Fully Clamped Cylindrical Shell	121
11.4 Conclusion	122
References	122
12 Linear/Nonlinear Reduced-Order Substructuring for Uncertainty Quantification and Predictive Accuracy Assessment	124
12.1 Introduction	124
12.2 Reduced-Order Linear/Linearized Substructure Models	125
12.2.1 Substructure Equations of Motion	125
12.2.2 Mass-Loaded Substructure Interfaces	125
12.2.3 Substructure Uncertainty Quantification	126
12.3 Reduced-Order Nonlinear Substructure Models	127
12.4 Substructure Coupling	129
12.4.1 Nodal Force Coupling	129
12.4.2 Removal of Added Mass (and Stiffness)	130
12.4.3 External Forces and Damping	131
12.5 Uncertainty Propagation	132
12.5.1 Linear Substructures	132
12.5.2 Nonlinear Substructures	133
12.6 Numerical Example	133
12.7 Conclusions	134
References	136
13 Damage Detection in an Energy Flow Model Including Parameter Uncertainty	137
13.1 Introduction	137
13.2 Theoretical Basis	138
13.2.1 Spectral Element Method	138
13.2.2 Polynomial Chaos Expansion	140
13.2.3 Moment Equations	140
13.3 Numerical Simulations	142
13.4 Final Remarks	144
References	145
14 A Coupled Approach for Structural Damage Detection with Incomplete Measurements	147
14.1 Introduction	147
14.2 Technical Background of Original Work	148
14.2.1 Dynamic Residual Formulation	148
14.2.1.1 Model Reduction	148
14.2.1.2 Matrix Disassembly	149
14.2.1.3 Estimating the Expanded Dynamic Residual	149
14.2.1.4 Mode Shape Expansion	150
14.2.1.5 Damage Location and Extent: MRPT	151
14.3 Example Application of Original Work	151
14.3.1 NASA Eight-Bay Truss	151
14.3.2 Spring Disassembly	151
14.3.3 Selection of Residual Basis Functions	152
14.3.4 Dynamic Residual Reduction/Expansion	153
14.3.5 Mode Shape Expansion	153
14.3.6 Damage Extent	154
14.4 Application of Original Method to Experimental Data	155
14.5 Assessment of Issues with Original Work	156
14.5.1 Model of Undamaged Structure	156
14.5.2 Data from Undamaged Structure	157
14.5.3 Reduction Transformation Matrix	157
14.5.4 Matrix Disassembly	157
14.5.5 Data from Damaged Structure	157
14.5.6 Dynamic Residual Expansion	157
14.5.7 Mode Shape Expansion	157
14.5.8 Damage Extent	158
14.6 Summary and Conclusions	158
References	158
15 Efficient and Robust Solution of Inverse Structural Dynamic Problems for Vibration Health Monitoring	160
15.1 Introduction	161
15.2 Analysis	162
15.2.1 Minimum Rank Perturbation Theory (MRPT)	162
15.2.2 Iterative MRPT	164
15.2.3 Dynamic Least Squares	166
15.3 Conclusions	168
References	170
16 Finite Element-Based Damage Detection Using Expanded Ritz Vector Residuals	172
16.1 Introduction	172
16.2 Mathematical Preliminaries	173
16.2.1 Analytical Ritz Vectors	173
16.2.2 Ritz Damage Residual	174
16.2.3 Experimental Ritz Vectors	174
16.2.4 Matrix Disassembly	175
16.2.5 Damage Residual Estimation with Reduced Measurements	176
16.3 Numerical Examples	177
16.3.1 Description of Test Model	177
16.3.2 Damage Residual Estimation	177
16.4 Summary	179
References	182
17 Proportional Damping from Experimental Data	183
17.1 Introduction	183
17.2 Viscous Damping	183
17.3 Proportional Damping Matrix	184
17.4 Proportional Damping Coeffcients	184
17.5 Least-Squared-Error Solution	185
17.6 Beam Structure	186
17.6.1 Modal Frequency and Damping	187
17.7 Two Extreme Cases	187
17.8 Using EMA Frequency and Damping	188
17.9 Using FEA Frequency and EMA Damping	189
17.10 Conclusions	190
References	190
18 Superior Damping of Hybrid Carbon Fiber Composites Grafted by ZnO Nanorods	191
18.1 Introduction	191
18.2 Experiment	192
18.2.1 Sample Preparation	192
18.2.2 Sample Characterization	193
18.2.3 Dynamic Mechanical Analysis (DMA)	193
18.3 Results and Discussion	193
18.3.1 SEM and XRD	193
18.3.2 DMA	193
18.4 Conclusion	195
References	196
19 Advanced Identification Techniques for OperationalWind Turbine Data	198
19.1 Introduction	198
19.2 The Micon 65/13M Wind Turbine and Field Test Description	199
19.3 Harmonic Component Removal Techniques	200
19.3.1 Time Synchronous Averaging	201
19.3.2 Removing Harmonics by Cepstrum Editing	202
19.4 Analysis of Data in Parked Conditions	203
19.5 Analysis of Operational Data	206
19.6 Conclusions and Way Forward	210
References	211
20 Tracking and Removing Modulated Harmonic Components with Spectral Kurtosis and Kalman Filters	213
20.1 Introduction	213
20.2 Detection of Modulated Sinusoidal Components	216
20.2.1 Definition of the Optimized Spectral Kurtosis Method	216
20.2.2 Testing of the OSK on an Experimental Bench	217
20.3 Tracking of Modulated Sinusoidal Components	218
20.3.1 Discrete State Space Formulation of an Amplitude and Frequency Modulated Sinusoid	218
20.3.2 Application to the Extended Kalman Filter	220
20.4 OSK and SEKF in Operation	222
20.4.1 Initializing the Series of Extended Kalman Filters	222
20.4.2 Numerical Results and Filtering Efficiency	223
20.5 Conclusion	225
References	225
21 Vibration Reduction of Brush Cutter	227
21.1 Introduction	227
21.2 Dynamic Characteristics of Brush Cutter	227
21.2.1 Measurement of ODS and FRF	228
21.2.2 Vibration Evaluation	229
21.2.3 Mode Contribution	229
21.3 Dynamic Characteristic of Brush Cutter	230
21.3.1 Structure of the Brush Cutter	230
21.3.2 Rubber Bush Hardness	230
21.3.3 Rubber Bush Modeling	231
21.3.4 Brush Cutter Modeling	232
21.4 Structural Modification	232
21.4.1 Rubber Bush Hardness Optimization	232
21.4.2 Rubber Bush Placement Optimization	233
21.4.3 Experimental Verification	234
21.5 Conclusions	234
References	235
22 Design of a Test Setup for Measuring Dynamic Stiffness of Vibration Isolators	236
22.1 Introduction	236
22.2 Conceptual Design of the Test Setup	237
22.3 Mathematical Model of the Test Setup	238
22.3.1 Equivalent Model of Upper Columns	239
22.3.2 Equivalent Model of the Crosshead and the Foundation	240
22.3.3 Equivalent Model of the Test Isolator	240
22.3.4 Equivalent Model of Force Distribution Plates, Specimen Flanges, and the Shaker	241
22.3.5 Equivalent Model of Lower Columns and Isolators Below the Test Setup	241
22.3.6 Equivalent Model of Decoupling Springs	241
22.4 Investigation of Modal Characteristics of the Test Setup	242
22.5 Virtual Tests on the Test Setup	242
22.5.1 Test Simulations with No Measurement Error Present	244
22.5.2 Test Simulations with Measurement Errors Present	245
22.6 Conclusion	248
References	248
23 An Impact Excitation System for Repeatable, High-Bandwidth Modal Testing of Miniature Structures	249
23.1 Introduction	249
23.2 Design and Construction of the Impact Excitation System	250
23.3 Model Development	251
23.3.1 Analytical Model of the Impact Excitation System	251
23.3.2 Impact Dynamics Model	252
23.3.3 Simulating the Tip Motion of the Impact Load Cell	252
23.4 Performance Evaluation of the Impact Excitation System	253
23.5 Summary and Conclusions	255
References	256
24 Replicating Aerodynamic Excitation in the Laboratory	258
24.1 Introduction	258
24.2 10 DOF Case Study: Applying Aerodynamic Excitation	259
24.3 Virtual Shaker Test	260
24.4 A New Approach to Replicating Aerodynamic Excitation in the Laboratory	264
24.5 Selection of Excitation Locations	268
24.6 Selection of Response Locations	268
24.7 Discussion	269
24.8 Conclusions	270
24.9 Further Work	270
References	270
25 A Systematic Approach to Modal Testing of Nonlinear Structures	272
25.1 Introduction	272
25.2 Brief Review of Some of the Methods Available in Literature	273
25.2.1 Homogeneity Method (Hg)	274
25.2.2 Hilbert Transform Method (HT)	274
25.2.3 Reverse Path Method (RP)	275
25.2.4 Singular Value Decomposition Method (SVD)	276
25.2.5 Complex Frequency Response Function Method (CFRF)	277
25.2.6 Nonlinear Normal Modes Experimental Technique (NNM)	277
25.2.7 Restoring Force Surface Method (RFS)	278
25.2.8 Nonlinear Output FRFs Method (NOFRFs)	279
25.3 Testing the Methods	279
25.3.1 Case N1	279
25.3.1.1 Detection	279
25.3.1.2 Characterisation	280
25.3.1.3 Quantification	281
25.3.2 Case N2	281
25.3.2.1 Detection	282
25.3.2.2 Localisation	282
25.3.2.3 Characterisation	284
25.3.2.4 Quantification	284
25.4 Conclusions and Future Work	284
References	285
26 Fiber Optics Sensing of Stressing and Fracturein Cylindrical Structures	286
26.1 Introduction	286
26.2 Scarc Specimen	287
26.3 FBG Strain Sensing and Crack Detection	288
26.4 Experiment	289
26.5 Results and Discussion	289
26.6 Discussion	290
26.7 Conclusion	291
References	292
27 Real-Time Damage Identification in Nonlinear Smart Structures Using Hyperchaotic Excitation and Stochastic Estimation	293
27.1 Introduction	293
27.2 Methodology	294
27.2.1 Stochastic Estimation Problem	294
27.2.2 The Extended Kalman-Bucy Filter	295
27.2.3 Tuned Hyperchaotic Excitation	296
27.3 Simulation Results	297
27.3.1 S-DOF Hysteretic Nonlinear Structure	297
27.3.2 Four-Story Shear-Beam Structure	300
27.4 Conclusions	302
References	303
28 Damage Detection Based on Electromechanical Impedance Principle and Principal Components	304
28.1 Introduction	304
28.2 Theoretical Base	305
28.2.1 Principal Component Analysis	305
28.2.2 Electromechanical Impedance Principle	306
28.3 Methodology and Experimental Setup	307
28.4 Results	307
28.4.1 Comparison Between PCC and EMI	309
28.5 Conclusion	311
References	312
29 Enhanced Modal Wavelet Analysis for Damage Detection in Beams	313
29.1 Introduction	313
29.2 Continuous Wavelet Transform Background	314
29.3 Modal-Wavelet Analysis Applied to Damage Detection	314
29.4 Experimental Testing	316
29.5 Results	317
29.6 Conclusions	318
References	319
30 Linear Projection Techniques in Damage Detection Under a Changing Environment	320
30.1 Introduction	320
30.2 Basic Scheme	321
30.2.1 Principal Component Analysis	321
30.2.2 Factor Analysis	322
30.3 Projection	322
30.3.1 Novelty Detection Using PCA	323
30.3.2 Novelty Detection Using FA	323
30.3.3 Summary	325
30.4 Simulation Example	325
30.5 Concluding Remarks	326
References	326
31 Modal Reduction Based on Accurate Input-Output Relation Preservation	328
31.1 Introduction	328
31.2 Method	329
31.2.1 Modal Truncation	329
31.2.2 Multiple Eigenvalues	330
31.2.3 Modal Dominancy Approach	330
31.2.4 Improved Modal Truncation Algorithm	331
31.3 Numerical Example	332
31.3.1 Aluminum Plate Model	332
31.3.2 Time Domain Input Signals	332
31.4 Results and Discussion	333
31.5 Concluding Remarks	336
References	337
32 Fast Precise Algorithm of Computing FRF by Considering Initial Response	338
32.1 Introduction	338
32.2 Fast Precise Algorithm of Computing FRF by Considering Initial Response in Continuous Exciting Test	341
32.3 Examples	343
32.3.1 A Real Test Example for Continuous Random Impact Shocking	343
32.3.2 A Real SISO Test Example for Continuous Random Exciting	345
32.4 Conclusions	346
References	347
33 Development of Full Space System Model Modes from Expansion of Reduced Order Component Modal Information	348
33.1 Introduction	348
33.2 Theoretical Background	349
33.2.1 Equations of Motion for Multiple Degree of Freedom System	349
33.2.2 Structural Dynamic Modification	350
33.2.3 Physical Space System Modeling	350
33.2.4 General Reduction/Expansion Technique	351
33.2.5 System Equivalent Reduction Expansion Process (SEREP)	351
33.2.6 Modal Assurance Criterion (MAC)	352
33.2.7 Pseudo Orthogonality Check	352
33.3 Methodology	352
33.4 Model Description	353
33.5 Cases Studied	353
33.5.1 Observations for All Cases	357
33.6 Conclusion	357
References	362
34 Damage Localization from the Image of Changes in Flexibility	363
34.1 Introduction	363
34.2 Influence Line Damage Localization Theorem	363
34.2.1 Practical Implementation of the Influence Line Damage Localization (ILDL) Theorem	365
34.3 Extension to the Output Only Case	365
34.4 Numerical Example	366
34.5 Experimental Illustration	367
34.6 Conclusions	367
Reference	369
35 Spectral Element Method for Cable Harnessed Structure	370
35.1 Introduction	370
35.2 The SEM for Euler-Bernoulli Beam with a Free-Free Boundary Condition	371
35.3 The SEM for Double Beam with a Free-Free Boundary Condition	373
35.4 Conclusion	377
References	378
36 Analytic Formula Derivation for a Rolling Tire with a Ring Model	381
36.1 Introduction	381
36.2 Theory	382
36.2.1 Brief Introduction of a Rotating Ring	382
36.2.2 Derive a Formula of a Rotating Ring with Mode Summation Method	382
36.2.3 Interpretation of the Derived Formula	384
36.3 Conclusion	386
References	387
37 Nonlinear Identification of the Viscous Damping of the Resistor for Nuclear Plants	388
37.1 Introduction	388
37.2 Tested Structure	389
37.3 Experimental Tests	389
37.4 Experimental Set-Up	390
37.5 Viscous Damping Assessment	390
37.6 Conclusions	397
References	397
38 Effect of Spin Speed on Stability Lobes in High Speed Machining	398
38.1 Introduction	398
38.2 Analytical Model	399
38.2.1 Spinning Timoshenko Beam Model	399
38.2.2 Coupling of Beams	400
38.2.3 Stability Lobes	401
38.2.4 Spindle Geometry	402
38.2.5 Results	403
38.3 Conclusions	405
References	405
39 Chatter Reduction in Turning by Using Piezoelectric Shunt Circuits	406
39.1 Introduction	406
39.2 Theory	408
39.3 Case Study	408
39.4 Conclusion	411
References	411
40 Damage Quantification from the Column Space of Flexibility Changes	412
40.1 Introduction	412
40.2 Damage Discontinuities and the Displacement Field Difference	412
40.3 Localization	413
40.4 Quantification	414
40.5 Inseparable Locations	415
40.6 Numerical Section	415
40.6.1 Example	415
40.7 Conclusions	416
References	416
41 State Estimate of Wind Turbine Blades Using Geometrically Exact Beam Theory	417
41.1 Introduction	417
41.2 State Observers	418
41.2.1 Review	418
41.2.2 Newton-Raphson Force Correction Observer	419
41.2.2.1 Discrete, LTI Reference Model	419
41.2.2.2 Nonlinear Reference Model	420
41.3 Physical Structure and Plant Model	422
41.4 Numerical Examples	423
41.4.1 NLBeam Plant with LTI SDOF Reference Model	423
41.4.1.1 Reference Model Description	423
41.4.1.2 Results	424
41.4.2 NLBeam Plant with NLBeam Reference Model	424
41.4.2.1 Reference Model Description	424
41.5 Summary	427
References	427
42 Damage Index Matrix: A Novel Damage Identification Method Using Hilbert-Huang Transformation	428
42.1 Introduction	428
42.2 Empirical Mode Decomposition	429
42.3 Hilbert Transform	431
42.4 Proposed Damage Index	431
42.5 Finite Element Validation of Proposed Method	432
42.6 Experimental Set-Up	435
42.7 Experimental Results	436
42.8 Conclusion	436
References	438
43 An Approach to the Moving Load Problem for Multiple Cracked Beam	440
43.1 Introduction	440
43.2 The Governing Equations of Dynamic System	441
43.3 Spectral Response of Cracked Beam to Arbitrary Moving Load	442
43.4 Results and Discussion	445
43.5 Conclusion	447
References	449
44 Detection of Structural Damage Through Nonlinear Identification by Using Modal Testing	450
44.1 Introduction	450
44.2 Theory	451
44.3 Experimental Studies	452
44.3.1 Experimental Study 1	452
44.3.2 Experimental Study 2	454
44.4 Conclusions	457
References	458
45 Vibration Fatigue Analysis of a Cantilever Beam Using Different Fatigue Theories	460
45.1 Introduction	460
45.2 Theory	461
45.3 Results	463
45.4 Conclusion	467
References	467
46 Automated Modal Analysis Based on Statistical Evaluation of Frequency Responses	468
46.1 Introduction	468
46.2 Theory	469
46.3 Case Studies	470
46.3.1 Plexiglass Plate	470
46.3.2 Dryer	472
46.4 Summary and Conclusion	474
References	475
47 The Modal Observability Correlation as a Modal Correlation Metric	476
47.1 Introduction	476
47.2 Theoretical Background	477
47.3 Observability Matrix	477
47.4 Modal Observability Correlation	478
47.5 Case Study	479
47.5.1 CompositePlate	479
47.5.2 Dryer	480
47.6 Discussion	480
47.7 Conclusion	482
References	483
48 A Modal Test Method Based on Vibro-acoustical Reciprocity	484
48.1 Introduction	485
48.2 Structural-Acoustic System Formulation	485
48.2.1 Eigenvalue Problem	485
48.2.2 FRFs	489
48.3 Modal Test Based on Vibro-Acoustic Reciprocity	490
48.4 Experimental Validation	491
48.4.1 Test Setup	491
48.4.2 Results and Discussion	492
48.5 Conclusion	494
References	497
49 Reactionless Test to Identify Dynamic Young's Modulus and Damping of Isotropic Plastic Materials	499
49.1 Introduction	499
49.2 Concept of Novel Reactionless DMA System	500
49.3 Material and Methods	500
49.4 Results	501
49.5 Conclusion and Further Work	503
References	504
50 Real-Time Modal Analysis of Shell-Shaped Objects Using High-Frame-Rate Structured-Light-Based Vision	505
50.1 Introduction	505
50.2 Fast Output-Only Modal Parameter Estimation	506
50.3 System Implementation	507
50.3.1 HFR Structured-Light-Based Vision Platform	507
50.3.2 The Implemented Algorithms	508
50.3.2.1 Measurement of 3D Vibrational Displacements	508
50.3.2.2 Fast Output-Only Modal Parameter Estimation	508
50.3.2.3 Damage Inspection	509
50.3.3 System Configuration	509
50.4 Experiment	509
50.5 Conclusions	511
References	511
51 Field and Numerical Testing of the BWE SchRs4600.50 Dynamic Behavior	512
51.1 Introduction	512
51.2 Numerical Calculations	513
51.3 Tests on the Machine	513
51.4 Correlation Between the Virtual Model and Experimental Model	516
51.5 Summary and Conclusions	519
References	519
52 Modal Analysis of Rotating Carbon Nanotube Infused Composite Beams	520
52.1 Introduction	520
52.2 Method	521
52.2.1 Composite Fabrication	521
52.2.2 Rotating Test Stand	522
52.2.3 Eigensystem Realization Algorithm (ERA)	523
52.3 Results and Discussion	523
52.3.1 Experimental Test Setup Validation	523
52.3.2 Operational Modal Analysis	525
52.4 Conclusions	527
References	527
53 Modal Analysis and Dynamic Monitoring of a Concentrating Solar Heliostat	529
53.1 Introduction	529
53.2 Test Structure, Instrumentation, and Data Acquisition	530
53.3 Modal Parameter Estimation	532
53.4 Results	534
53.5 Summary and Future Work	537
References	537
54 Identification of Stability Cutting Parameters Using Laser Doppler Vibrometry	538
54.1 Introduction	538
54.2 Modal Parameters of Thin-Walled Structure	539
54.3 Time Varying Modal Behavior of the Thin Wall During the Machining Processes	540
54.4 Conclusion	541
References	545
55 System Identification Using Kalman Filters	546
55.1 Introduction	546
55.2 Problem Statement	547
55.3 System Identification	547
55.3.1 Generalities	547
55.3.2 Step 1: Measurements	548
55.3.3 Step 2: Model Construction	548
55.3.3.1 The Reduced-Order Model (ROM)	548
55.3.3.2 Setting of Extended Kalman Filter (EKF)	549
55.3.3.3 Setting of Unscented Kalman Filter (UKF)	549
55.3.4 Basic Formulation of Kalman Filters	549
55.3.4.1 Extended Kalman Filter (EKF)	549
55.3.4.2 Unscented Kalman Filter (UKF)	550
55.4 Numerical Results	550
55.4.1 Filtering Step	551
55.4.2 Sensitivity Analysis	551
55.4.2.1 Sensitivity to the State Model Covariance	551
55.4.2.2 Sensitivity to the Observation Covariance	552
55.4.2.3 Sensitivity to the Initial State Estimate Covariance	554
55.5 Conclusions and Future Work	555
A.1 Model Construction Step Using EKF	556
B.1 EKF and UKF Algorithms	557
B.1.1 Extended Kalman Filter (EKF)	557
B.1.2 Unscented Transform (UT)	557
B.1.3 Unscented Kalman Filter (UKF)	558
References	558
56 Identification of Time-Varying Nonlinear Systems Using Differential Evolution Algorithm	559
56.1 Introduction	559
56.2 Differential Evolution for Time-Varying Nonlinear Systems	560
56.2.1 Classical Differential Evolution	560
56.2.2 Differential Evolution with Time-Varying Cost Function	561
56.2.2.1 Cost Function in DE for Time-Varying Systems	561
56.2.2.2 Initialisation of DE for Time-Varying Systems	562
56.3 Results of Identification with Simulated Noise-Free and Noisy Data	562
56.3.1 Simulation Set-Up	562
56.3.2 Identification of Time-Varying System with Coulomb Friction Nonlinearity Using Classical DE Algorithm	563
56.3.3 Identification of Time-Varying System with Coulomb Friction Using Modified DE Algorithm	563
56.3.3.1 Results with Noise-Free Measurements	563
56.3.3.2 Results with Noisy Measurements	564
56.3.3.3 Discussion of the Results	565
56.4 Conclusions and Future Work	566
References	566
57 Experimental Verification and Improvement of Dynamic Characterization Method for Structural Joints	568
57.1 Introduction	568
57.2 Theoretical Formulation	569
57.2.1 Identification of Dynamic Properties of Joints Using FRF Decoupling	569
57.2.2 Estimation of FRFs for RDOF and Unmeasured Coordinates	570
57.2.3 Optimization and Joint Parameter Updating	570
57.3 Experimental Studies	571
57.3.1 Experimental Study I: Beams Connected with M1035 Hexagonal Bolt	571
57.3.2 Experimental Study II: Beams Connected with M835 Hexagonal Bolt	574
57.3.3 Experimental Study III: Beams Connected with M630 Hexagonal Bolt	576
57.3.4 Effect of Bolts Size on Dynamic Properties of the Bolted Joint	577
57.4 Discussions and Conclusions	578
References	579
58 Transfer Functions to Measure Translational and Rotational Velocities with Continuous-Scan Laser Doppler Vibrometry	580
58.1 Introduction	580
58.2 Theoretical Basis	581
58.2.1 Periodic Model of CSLDV Measurement	581
58.2.2 Harmonic Transfer Function of CSLDV	582
58.2.3 Measuring Rotational Velocities	584
58.2.4 Computing Curvature	586
58.3 Experimental Setup and Speckle Noise	586
58.4 Deflection Mode Shapes	589
58.5 Rotational Velocity and Local Slope	590
58.6 Conclusion	594
References	597
59 Empirical Slow-Flow Identification for Structural Health Monitoring and Damage Detection	599
59.1 Introduction	599
59.2 Nonlinear System Identification of a Vibro-Impact Beam	600
59.3 Applications of NSI Results to Damage Identification	603
59.4 Conclusions	605
References	605
60 Continuous Scanning for Acoustic Field Characterization	607
60.1 Introduction	607
60.2 Methodology	608
60.3 Experimentation	609
60.3.1 Experimental Setup	609
60.3.2 Testing Procedures and Preliminary Results	610
60.3.2.1 Obtaining Pressure Distributions Using a Scanning Microphone	611
60.3.2.2 Spectrum Data Gathered via Continuous Scan	612
60.4 Summary	614
References	616
61 Operating Deflection Shapes of a Violin String via High Speed/High Resolution Videography	619
61.1 Introduction	619
61.2 Testing	620
61.3 Results	623
61.4 Conclusions	625
References	626
62 Automated Measurement Grid Generation for Scanning Laser Doppler Vibrometers	627
62.1 Introduction	627
62.2 Scanning LDV System	628
62.3 Automated Grid Generation	628
62.4 SLDV Continous Area Scan	629
62.5 Target Identification	629
62.6 Boundary Definition	630
62.7 Grid Generation	632
62.8 Conclusion	635
References	635
63 Mode Filtering of Continuous Scanning Laser Doppler Vibration Data	636
63.1 Introduction	636
63.2 Description of the Procedure for ODS and Resonance Frequency Extraction	637
63.3 Algorithm Testing	639
63.3.1 Analysis of Results from Simulated Data	639
63.4 Conclusion	640
References	641
64 The Characterization of the Time Delay Problem in Hardware in the Loop System Applications	642
64.1 Introduction	642
64.2 Investigation of Factor for Time Delay	643
64.2.1 Real-Time System Process	643
64.2.2 HIL Modeling	645
64.2.3 Ideal HIL Response	646
64.2.4 Real HIL Response	647
64.3 HIL Time Delay Validation Setup	647
64.3.1 HIL Response Sequences Validation	647
64.3.2 Experimental HIL System Setup	648
64.3.3 Virtual HIL System Setup	648
64.3.4 Example 1: Unstable with Time Delay	649
64.3.5 Example 2: Stable with Time Delay	649
64.4 Numerical HIL Simulation	650
64.4.1 HIL Simulation of Example 1	650
64.4.2 HIL Simulation of Example 2	650
64.5 Experimental HIL Realisation	651
64.5.1 HIL Experimental of Example 1	651
64.5.2 HIL Experimental of Example 2	651
64.6 Concluding Remarks and Future Work	652
References	652
65 Optimal Placement of Piezoelectric Patches on a Cylindrical Shell for Active Vibration Control	653
65.1 Introduction	653
65.2 Methodology	654
65.3 Application to Cylinder Geometry	655
65.4 Conclusion	660
References	661
66 Adaptive Feedback Linearisation and Control of a Flexible Aircraft Wing	662
66.1 Introduction	663
66.2 The Aeroservoelastic Model	663
66.2.1 Co-ordinate Transformation	665
66.2.2 Forcing Terms	666
66.2.3 Including Nonlinearity	666
66.3 Numerical Simulation (Part 1)	666
66.3.1 Model Dimensions and Parameters	667
66.3.2 Airspeed vs. Natural Frequency and Airspeed vs. Damping Ratio Plots	667
66.3.3 Linear Time-Domain Response	667
66.3.4 Nonlinear Time-Domain Response	669
66.4 Feedback Linearisation	670
66.4.1 Nonlinear State-Space Model, Choosing Outputs and Finding Relative Degree	670
66.4.2 Linearising the System	671
66.5 Numerical Simulation (Part 2)	672
66.6 Uncertainty in the Nonlinearity Parameters	673
66.7 Numerical Simulation (Part 3)	675
66.8 Adaptive Feedback Linearisation	675
66.9 Numerical Simulation (Part 4)	676
66.10 Conclusions	677
References	678
67 Limit Cycle Assignment in Nonlinear Aeroelastic Systems Using Describing Functions and the Receptance Method	679
67.1 Introduction	679
67.2 Theory	680
67.2.1 Limit Cycle Prediction Based on Describing Functions and Sherman-Morrison Formula	680
67.2.2 Limit Cycle Assignment	682
67.2.3 A New Form of Limit Cycle Stability Criterion for Closed-Loop System	682
67.2.4 Optimisation of Control Gains	684
67.3 Numerical Example	685
67.3.1 Binary Aeroelastic Model with Cubic Stiffness in Pitch	686
67.3.2 Binary Aeroelastic Model with Bilinear Stiffness in Pitch	687
67.4 Discussion and Conclusions	690
References	691
68 Investigation of an Active Structural Acoustic Control System on a Complex 3D Structure	692
68.1 Introduction	692
68.2 Vibro-Acoustic Model and Analysis	693
68.3 Design and Simulation of the ASAC System	695
68.4 Noise Reduction Performance of the ASAC System	696
68.5 Conclusion	696
References	697
69 Development of a Stabilized Pan/Tilt Platform and the State of the Art	699
69.1 Introduction	699
69.2 Rigid Body Dynamıcs	699
69.3 Structural Dynamics Response	700
69.4 Servocontrol	702
69.5 Inertial Navigation and Sensor Fusion	703
69.6 Stabilization Control	704
69.7 Performance of the Prototype	704
69.8 Results	705
References	705
70 Dynamic Equations for an Anisotropic Cylindrical Shell	707
70.1 Introduction	707
70.2 Problem Formulation	708
70.3 Results for a Ring	711
70.4 Conclusions	713
References	717
71 Expansion of Nonlinear System Response Using Linear Transformation Matrices from Reduced Component Model Representations	718
71.1 Introduction	719
71.2 Theory	720
71.2.1 Model Reduction and Expansion	720
71.2.2 General Transformation	721
71.2.3 System Equivalent Reduction Expansion Process (SEREP)	721
71.2.4 System Modeling and Mode Contribution	722
71.2.5 Mode Shape and Time Response Data Expansion/Smoothing Process	726
71.2.6 Use of Mode Contribution Matrix for Expanding Time Response Data	727
71.3 Model Description and Cases Studied	728
71.3.1 Model Description	728
71.3.2 Analytical Case Study	732
71.3.3 Experimental Case Study	736
71.4 Observations	741
71.5 Conclusion	741
References	743
72 Explicit Construction of Rods and Beams with Given Natural Frequencies	745
72.1 Introduction	745
72.1.1 Main Ideas of the Reconstruction Procedure	745
72.1.2 Reduction to Normal Form	746
72.1.3 The Darboux Lemma	747
72.1.4 Quasi-isospectral Potentials	747
72.1.5 Quasi-isospectral Rods	750
72.1.6 Constructing Rods with a Given Set of Dirichlet Eigenvalues	751
72.2 Extensions and Generalizations	752
References	752
73 A Metric for Modal Truncation in Model Reduction Problems Part 1: Performance and Error Analysis	754
73.1 Introduction	754
73.2 Problem Statement	755
73.2.1 The Quadratic Approximation Problem	756
73.3 Modal Dominancy Metrics	757
73.3.1 A Dominancy Metric Based on Modal Contribution to Transfer Function H2 -Norm	758
73.3.2 Performance and Error Analysis	759
73.3.3 On the Question of Optimality	760
73.4 Conclusion	761
References	761
74 A Metric for Modal Truncation in Model Reduction Problems Part 2: Extension to Systems with High-Dimensional Input Space	762
74.1 Introduction	762
74.2 Metric Non-uniqueness in Multiple Eigenvalue Problems	763
74.3 Incorporating Input Information in Truncation Decisions	765
74.3.1 Modal Truncation Based on Spatial and Spectral Properties of the Input	765
74.3.2 Algorithm of the Improved Modal Approach	766
74.4 Numerical Example	767
74.4.1 Railway Track Model Subjected to a Moving Input Loading	767
74.4.2 Results and Discussion	767
74.5 Conclusion	769
References	769
75 On Gramian-Based Techniques for Minimal Realization of Large-Scale Mechanical Systems	770
75.1 Introduction	770
75.2 Background Theory	771
75.3 Non-minimal State Space Realizations	773
75.4 Large-Scale State Space Realizations	774
75.5 A Hybrid Modal-Balanced Algorithm	775
75.6 Numerical Examples	775
75.6.1 A 10-DOF Double Symmetric Problem	776
75.6.2 A 885-DOF Plate Problem	777
75.7 Conclusion	778
References	778

RkJQdWJsaXNoZXIy MTMzNzEzMQ==