Nonlinear Structures & Systems, Vol. 1

Front Cover	1
Conference Proceedings of the Society for Experimental Mechanics Series	2
Nonlinear Structures & Systems, Vol. 1	4
Preface	6
Contents	8
Linear and Nonlinear Response of a Continuous-Interface BARC: FEA Prediction and Test	10
Introduction	10
Creating a Finite Element Model of the BARC	11
Nonlinear Predictions from the FEM	12
Physical Testing	15
Linear Testing and Data Analysis	16
Nonlinear Testing and Data Analysis	16
Comparing Test Results and Predictions	19
Linear Mode Shapes and Natural Frequencies	19
Nonlinearity	20
Conclusion	21
Appendix	22
www.FreeDyn.at – A free, GUI based multi-body dynamics software for stand-alone use and with C API for linking it to Python, Matlab or custom code	24
Introduction and Theoretical Background	24
Available Modelling Elements	25
Stand-Alone Software or C-Api	25
Python Example	26
Additonal Examples	28
Nonlinear Frequency Response Surfaces, Part I: Theoretical Formulation	30
Introduction	30
Theoretical Formulations of the Nonlinear Frequency Response Surface	31
Linear frequency response surface (LFRS)	31
Nonlinear Frequency Response Surface (NFRS)	31
Generation of the NFRS Using the Experimental Modal Analysis	33
EMA using the modified-Dobson method	33
Application to an experimental blind case	34
Final remarks	34
Conclusions	35
Fatigue Damage Potential in a Nonlinear Dynamical System with Isolated Resonances	36
Introduction	36
Methodology and System Model	37
Fatigue Damage Analysis	37
Conclusions	38
Robust Optimization of Surface Topology for Jointed Connections	40
Introduction	40
Modeling	41
Results	44
Conclusion and Future Work	46
References	47
Nonlinear Vibration Control on Complex Structures via Model Predictive Control Exploiting Koopman Model	50
Introduction	50
Experimental Set-up of Benchmark Structure	50
Koopman Linear reconstruction and Control objective	51
Virtual Experimental results	51
Conclusion	52
Stochastic Dynamics and Surrogate Modeling for Nonlinear Aerospace Nozzle Systems with Partial Observations	54
Introduction	54
Background	54
Analysis of the Results	55
Conclusion	56
Industrial Applications of Nonlinear Modal Modeling: Two Case Studies	58
Introduction	58
Nonlinear Modal Models	59
Test Methods and Identification	59
Sine Beats	60
Nonlinear Force Appropriation	60
Nonlinear Modal Model Identification	61
Case Studies: Industrial Applications of the NLMM	62
Case Study 1	63
NLMM Identification	63
Case Study 2	65
Nonlinear Modal Model Identification	66
NFA Results	67
Summary	69
Decoupling of Nonlinear Substructures using Quasi-linear Frequency Response Functions	72
Introduction	72
Theory	73
Systems Coupled From A Single Point	74
Systems Connected From Multiple Points	75
Lumped parameter system	75
Continuous system	76
Conclusion	77
An Overview of ANSYS Harmonic Balance Method: Current Capabilities and Future Directions	80
Introduction	80
Harmonic Balance Method Overview	81
Overview of the Convergence Improvement Techniques	81
Application of the Ansys-HBM to a Benchmark Example	82
Conclusions	83
Derivative-Free Arclength Control-Based Continuation for Secondary Resonances Identification	86
Introduction	86
Background	87
Analysis	89
Conclusion	91
Modelling a Nonlinear Single-Degree-of-freedom System from Experimental Data using Lagrangian Neural Networks	92
Introduction	92
Conclusions and Future Work	95
Computing Periodic Responses of Highly Flexible Beams Modelled under the SE(3) Lie Group Framework with Multiple Shooting	96
Introduction	96
Multiple Shooting Formulation	97
Adaptation of the Multiple Shooting Method to Lie Group Formulations	98
Application of Multiple Shooting to 2D Beams	99
An Investigation of Nonlinear Solution Techniques for SSM-Reduced Mechanical Systems	102
Introduction	102
Direct Parameterization of Invariant Manifolds	103
Practical issues	104
Nonlinear Solvers for Computing Periodic Solutions	105
Harmonic Balance via Alternating Frequency-Time	105
Orthogonal Collocation	105
Single Shooting	106
Numerical Continuation	106
Application and Discussion of Results	107
Harmonic Balance via Alternating Frequency-Time	108
Orthogonal Collocation	109
Single Shooting	109
Conclusion	110
Flutter Analysis of Control Surface Free-play by Using a 3-DOF Airfoil Model	112
Introduction	112
Mathematical Modelling	113
Nonlinear Flutter Solution	115
Results	116
Conclusion	118
The Nonlinear Restoring Force Method: An Overview with Numerical and Experimental Applications	120
Introduction	120
Methodology, Background Theory, and Limitations	121
Numerical Example: A Three Storey Building with a Localised Nonlinearity	122
Experimental Validation: Identification of Smooth and Non-Smooth Nonlinearities	124
Conclusions	128
Data Availability	129
Forced Response of Nonlinear Systems Under Multi-Frequency Excitations by Using Harmonic Balance Method	130
Introduction	130
Mathematical Modeling	131
Harmonic Balance Method For Multi-Frequency Excitation	132
Results and Discussion	133
Conclusion	135
Finding the Limits of Beam Elements: Modeling Bolted Joints as an Effective Joint Region	138
Introduction	138
Experimental setup	139
Finite element model updating	140
Results	142
Conclusion	144
Acknowledgement	145
Design of a Tuned Vibration Absorber with Friction Contact for High Location Ratio Application	146
Introduction	146
Methods	148
Theory	148
Model Creation and Validation	149
Location Ratio	151
SDoF TVA Directional Analysis	152
TVA Design	152
Combined BA-TVA Systems and TVA Tuning	154
Results	156
Linear Simulations	156
Nonlinear Simulations	156
Discussion	159
Design Considerations	160
Future Work	162
Appendix	163
Topology Optimization of Isolated Response Curves in 3D Geometrically-nonlinear Beam	166
Introduction	166
Methodology	167
Coupled Harmonic Balance based approach for the non-linear dynamics of spur gear pairs	170
Introduction	170
Methodology	171
Single DOF model	172
Contact model	173
Results and discussion	174
Non-linear forced responses	175
Contact force	176
Conclusions	178
Multi-level Stochastic Model Identification of Complex Aeroelastic Systems Considering Aerodynamic Nonlinearities	180
Introduction-10pt	180
Methodology	181
Results	181
Conclusion	183
Acknoledgements	183
Resonance Tracking of Nonlinear Structures by Amplitude Controlled Sine-Dwell Testing	184
Introduction	184
Experimental Setup and control strategy	185
Experimental Results	186
Conclusion	188

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