Nonlinear Structures & Systems, Volume 1

Preface	6
Contents	7
1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model	10
1.1 Introduction	10
1.2 Machine Learning for Structural Dynamics	12
1.3 A Three-Storey Building Dataset	13
1.4 Statistics of the Model Gradients as a Nonlinearity Metric	14
1.5 Conclusions	17
References	18
2 Robust Identification of Nonlinear Oscillators from Frequency Response Data	19
2.1 Introduction	19
2.2 System Identification	20
2.3 Results	20
2.4 Conclusions	21
References	21
3 Creating Data-Driven Reduced-Order Models for Nonlinear Vibration via Physics-Informed Neural Networks	22
3.1 Introduction	22
3.2 Methodology	23
3.2.1 Example: Five-Degree-of-Freedom, Nonlinear Mass-Spring Model	24
3.2.2 Data Generation	24
3.2.3 Long Short-Term Memory	25
3.2.4 Physics-Informed Loss Function	26
3.3 Conclusions	26
References	27
4 Effect of Structural Parameters on the Nonlinear Vibration of L-Shaped Beams	29
4.1 Introduction	29
4.2 Background	30
4.2.1 Formulation of the L-Shaped Beam	30
4.2.2 Discretization of the Nonlinear PDEs by Using Galerkin's Method	32
4.2.3 Multiharmonic Harmonic Balance Method (HBM)	33
4.3 Results and Discussions	34
4.3.1 Linear Model Results	34
4.3.2 Case Studies	35
4.4 Conclusion	37
References	38
5 Importance of Virtual Sensing and Model Reduction in the Structural Identification of Bolted Assemblies	39
5.1 Introduction	39
5.2 Methodology	39
5.3 Analysis and Discussion	40
5.4 Conclusion	41
References	41
6 On the Harmonic Balance Method Augmented with Nonsmooth Basis Functions for Contact/Impact Problems	43
6.1 Introduction	43
6.2 Nonsmooth Galerkin Formulation	44
6.3 Least-Squares Regression Analysis	44
6.4 Conclusion	45
References	45
7 Periodic Response Prediction for Hybrid and Piecewise Linear Systems	46
7.1 Introduction	46
7.2 Periodic Response of Harmonically-Excited Time-Switched Hybrid Systems	47
7.3 Periodic Response of Harmonically-Excited Piecewise Linear Systems	50
7.4 Discussion and Conclusion	53
References	53
8 A Tutorial on Data-Driven Methods in Nonlinear Dynamics	55
8.1 Introduction	55
8.2 Bayesian Inference and System Identification	57
8.3 System Identification Using Markov Chain Monte Carlo	59
8.4 Case Study in Parameter Estimation: The Duffing Oscillator	61
8.5 Model Selection and Approximate Bayesian Computation	63
8.6 Case Study in Equation Discovery: Hysteretic Systems	66
8.7 Coloured Boxes and Physics-Informed Machine Learning	69
8.7.1 Case Study: Prior Mean Functions—Residual Modelling	71
8.8 Conclusions	72
References	73
9 Modeling Nonlinear Structures Using Physics-Guided, Machine-Learnt Models	75
9.1 Introduction	75
9.2 Background	76
9.3 Introducing Nonconservative Forces	76
9.4 Experimental Analysis	76
9.5 Exploiting Known Physics	78
References	78
10 Bypassing the Repeatability Issue in Nonlinear Experimental Modal Analysis of Jointed Structures by Using the RCT-HFS Framework	79
10.1 Repeatability Issue	79
10.2 Application of the RCT-HFS Framework to the Orion Beam	80
10.3 Discussions and Conclusions	83
References	84
11 Towards Exact Statistically Independent Nonlinear Normal Modes via the FPK Equation	85
11.1 Introduction	85
11.2 The Fokker-Planck-Kolmogorov Equation	86
11.3 Direct NNMs in a Single Dimension	87
11.3.1 A Cautionary Result	91
11.4 Towards Direct MDOF NNMs	93
11.5 Discussion	94
References	94
12 Simulating Nonlinear Beating Phenomena Induced by Dry Friction in Dynamic Systems	96
12.1 Introduction	96
12.2 Background	97
12.2.1 Lumped Parameter Model	97
12.3 Analysis	98
12.3.1 Numerical Integration Scheme	98
12.4 Conclusion	99
References	99
13 Case Study on the Effect of Nonlinearity in Dynamic Environment Testing	100
13.1 Introduction	100
13.2 Setting of Problem	101
13.3 Results	102
13.4 Conclusions	103
References	103
14 Strategies for Improving the Comparison of Frequency Response Functions with Similarity Metrics	104
14.1 Introduction	104
14.2 Simulation	106
14.3 Experimental Validation	108
14.4 Conclusions	111
Appendix	111
References	112
15 Resonant Characterization of Nonlinear Structures in the Co-existence of Multiple Resonant Components	113
15.1 Introduction	113
15.2 Methodology	114
15.3 Numerical Illustrations on a Two-DOF System	115
15.3.1 Two-Component Single Harmonic Balance Results	116
15.4 Conclusions	118
References	118
16 Derivative-Less Arclength Control-Based Continuation for the Experimental Identification of Nonlinear Frequency Responses	120
16.1 Arclength Continuation: The Basic Idea	120
16.2 Numerical Example	122
16.3 Conclusion	125
References	125
17 Experimental Modal Analysis of Structures with High Nonlinear Damping by Using Response-Controlled Stepped-Sine Testing	126
17.1 Introduction	126
17.2 Nonlinear Experimental Modal Analysis with the RCT-HFS Framework	127
17.3 Experiment	128
17.4 Discussions and Conclusions	132
References	132
18 The TRChallenge: Experimental Quantification of Nonlinear Modal Parameters and Confrontation with the Predictions	134
18.1 Introduction	134
18.2 Experimental Setup and Test Strategies	135
18.3 Results	136
18.4 Conclusion	137
References	137
19 Using Abaqus with Python to Perform QSMA on the TMD Structure	138
19.1 Introduction	138
19.2 Theory	139
19.2.1 Using Python to Perform QSMA	140
19.2.1.1 Using Abaqus's Restarts	141
19.2.1.2 Rough Friction vs. Lagrange Friction	141
19.3 Case Study 1: Stacked Beam	142
19.3.1 Application of Quasi-static Modal Analysis	142
19.3.1.1 Post-Processing Results from the Static Analysis	143
19.3.2 Validation of Pseudo-inverse Approach	143
19.4 Case Study 2: 2D TMD Benchmark Structure-10pt	144
19.4.1 Results	145
19.5 Case Study 3: 3D TMD Benchmark Structure	146
19.6 Conclusions	147
Appendix	147
References	154
20 A Novel Approach for Local Structural Modification of Nonlinear Structures	156
20.1 Introduction	156
20.2 Theory	157
20.3 Case Studies	158
20.4 Conclusions	161
References	161
21 Model Validation of a Modular Foam Encapsulated Electronics Assembly with Controlled Preloads via Additively Manufactured Silicone Lattices	162
21.1 Introduction	162
21.2 Geometry	163
21.3 Materials	164
21.4 Homogenized Material Paramaterization for DIW Lattice Structures	165
21.5 Experimental Methods	165
21.6 Finite Element Analysis	166
21.7 Results	168
21.8 Conclusion	170
References	171
22 Characterizing the Dynamic Response of a Foam-Based Testbed with Material, Geometric, and Experimental Uncertainties	172
22.1 Introduction	172
22.2 Methods	173
22.3 Results and Analysis	176
22.4 Discussion	180
22.5 Conclusion	181
Appendix	182
References	184
23 Experimental Investigation on Frictional Interfaces of a Bolted Flange System	185
23.1 Introduction	185
23.2 Experimental Setups	186
23.3 Results and Discussion	187
23.4 Conclusion	187
References	188
24 Estimation of Wheel Center Forces of a Car, Without Neither Load Sensor Nor Strain Gauge Measurements When Crossing a Groove on the Road	189
24.1 Introduction	189
24.2 Background	190
24.2.1 Rotation Representation	190
24.2.2 Multi-body Equations	190
24.2.3 The Constraints Equations	191
24.3 Kalman Filtering of the Multi-body Model	191
24.3.1 The Augmented and Constrained Extended Kalman Filter (ACEKF)	191
24.3.2 Kalman Prediction	192
24.3.3 Kalman Correction	192
24.3.4 Kalman Modifications	193
24.4 Analysis	193
24.4.1 Model Studied	193
24.4.2 Experimentation of Alternative Kalman Filters	195
24.5 Conclusion	196
References	196
25 Nonlinear Dynamics, Continuation, and Stability Analysis of a Shaft-Bearing Assembly	197
25.1 Introduction	197
25.2 System Modeling and Numerical Methods	198
25.3 Frequency Response Analysis	198
25.4 Conclusions	199
References	199
26 Quantification of Amplitude- and Rotation Speed-Dependent Nonlinearity of Machine Tool Spindles	200
26.1 Introduction	200
26.2 Selected Results	200
26.3 Conclusions	202
References	202
27 Toward Active Control of Limit Cycle Oscillations in an Aeroelastic Wing Using a Variable Frequency Flow Disturbance Generator	203
27.1 Introduction	203
27.2 Methodology	204
27.3 Results and Analysis	206
27.4 Planned Future Work	207
27.5 Conclusions	210
References	211
28 Experimental Parameter Identification of Nonlinear Mechanical Systems via Meta-heuristic Optimisation Methods	212
28.1 Introduction	212
28.2 Experimental Test Rig and Nonlinear Analysis	213
28.3 Model Updating of the Underlying Linear System	214
28.4 Nonlinear Model Updating	216
28.5 Conclusion	218
References	219
29 Investigation of the Nonlinear Dynamics of a Particle-Damped Slender Beam by Experimental Continuation	221
29.1 Introduction	221
29.2 Theoretical Background of Experimental Continuation	221
29.3 Experimental Setup	222
29.4 Results	222
References	223
30 Identification of Nonlinear Characteristics of an Additive Manufactured Vibration Absorber	224
30.1 Introduction	224
30.2 Experimental Test Rig	225
30.3 Linear System Characterisation	225
30.4 Nonlinear System Characterisation	226
30.5 Conclusion	229
References	230
31 Resonant Vibration Absorbers with Impacts	231
31.1 Introduction	231
31.2 Methodology	232
31.3 Results and Discussion	232
31.4 Conclusions	233
References	235
32 Modeling and Verifying the Dynamic Response of Layered Plate Damping Systems	236
32.1 Introduction	236
32.2 Background	237
32.3 Experimental Testing Methodology	238
32.3.1 Test Setup and Considerations	238
32.3.2 Test Procedure	239
32.4 Finite Element Procedure	242
32.4.1 Model Setup	242
32.4.2 Mesh Convergence and Material Property Estimation	242
32.4.3 Simulation Steps	243
32.5 Results	245
32.5.1 Numerical and Experimental Comparison	245
32.5.2 Experimental Analysis	246
32.6 Conclusions	247
References	251
33 State-Space Modeling of Nonlinear Electrostatic Transducers and Experimental Characterization Using LDV	252
33.1 Introduction	252
33.2 Analysis	253
33.3 Conclusions and Future Work	257
References	257

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