Nonlinear Structures & Systems, Volume 1

Preface	6
Contents	7
Pre-test Predictions of Next-Level Assembly Using Calibrated Nonlinear Subcomponent Model	9
1 Introduction	9
2 Theory	11
2.1 Nonlinear Hurty/Craig-Bampton Reduction	11
2.2 Multi-harmonic Balance	12
3 Fixture-Pylon Model Calibration	12
3.1 Fixture-Pylon Finite Element Model	13
3.2 Extracting Backbone Curves from Experimental Stepped-Sine Data	14
3.3 Calibration of Nonlinear Elements	14
3.4 Stepped-Sine Validation	15
4 Wing-Pylon NNM Computation	17
4.1 Wing-Pylon Finite Element Model	17
4.2 NNM 1 Computation	18
4.3 NNM 2 Computation	18
5 Conclusions	21
References	21
Nonlinear Variability due to Mode Coupling in a Bolted Benchmark Structure	22
1 Introduction	22
2 Experimental Setup and Procedure	23
3 Results	23
4 Conclusion	25
References	25
Nonlinear Dynamic Analysis of a Shape Changing Fingerlike Mechanism for Morphing Wings	26
1 Introduction	26
2 Theory: Quasi-Static Modal Analysis	28
3 Finite Element Model of Morphing Wing	29
4 Simulated Results of Morphing Wing Fem	30
4.1 Static Preload	30
4.2 Quasi-Static Modal Analysis	33
4.3 Reduced Order Model	35
5 Conclusions and Future Work	36
References	37
Evaluation of Joint Modeling Techniques Using Calibration and Fatigue Assessment of a Bolted Structure	39
1 Introduction	39
2 Hardware Description	39
2.1 Assembly Hardware	40
3 Experimental Data and Analysis	41
3.1 Free-Free Modal Data	41
3.2 Fixed Base Modal Data	42
3.3 Additional Fixed Base Testing and Characterization of Axial Mode	43
4 Structural Dynamic Modeling	46
4.1 Model 1: Solid Bolt and Tied Joint Interface	46
4.2 Model 2: Tied Joint Bolt and Interface	47
4.3 Model 3: Single Tied Joint	47
4.4 Model 4: Tied Data	47
5 Model Updating	48
5.1 Initial Study	48
5.2 Free-Free Comparison	49
5.3 Fixed Base Comparison	51
6 Initial Fatigue Assessment	52
6.1 Background	52
6.2 Evaluating Uniaxial Fatigue	52
7 Joint Stiffness Comparison	53
7.1 Analytical Calculations	53
7.2 Linear Structural Dynamic Analysis	54
7.3 Nonlinear Solid Mechanics Analysis	55
8 Conclusion	58
References	58
A Non-Masing Microslip Rough Contact Modeling Framework for Spatially and Cyclically Varying Normal Pressure	59
1 Introduction	59
2 System Modeling	60
3 Asperity Contact Modeling	61
4 Results	63
References	64
Finite Elements and Spectral Graphs: Applications to Modal Analysis and Identification	66
1 Introduction	66
2 Formulation and Approach: Discretization of the Wave Equation	67
2.1 Quick Recap of Linear Finite Elements	67
2.2 Discretization on the Graph Domain	68
3 Results and Conclusions	70
4 Future Work	70
References	71
Effects of the Geometry of Friction Interfaces on the Nonlinear Dynamics of Jointed Structure	72
1 Introduction	72
2 Methodoloy	73
2.1 Step 1: Nonlinear Static Analysis	74
2.2 Step 2: Refined Contact Analysis	74
2.3 Step 3: Nonlinear Dynamic Analysis	74
3 Case Study	75
4 Results	76
5 Conclusion	78
References	79
Bifurcation Analysis of a Piecewise-Smooth Freeplay System	80
1 Introduction	80
2 System's Modeling	81
3 Nonlinear Characterization	81
4 Conclusions	81
References	82
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations	83
1 Introduction	83
2 System Modeling	84
3 Effectiveness of Continuous Representations for System with Freeplay Nonlinearity	85
4 Conclusions	85
References	85
Model Updating and Uncertainty Quantification of Geometrically Nonlinear Panel Subjected to Non-uniform Temperature Fields	86
1 Introduction	86
2 Theory	87
2.1 Geometrically Nonlinear Finite Element Model	87
2.2 Modal Analysis About Thermal Equilibrium	88
3 Model Correlation of Curved Panel	88
3.1 Target Experimental Data	88
3.2 Temperature Field Mapping to FE Model	88
3.3 Model Updating of Curved Panel at Room Temperature	90
3.4 Modal Analysis of Curved Panel Subjected to Localized Central Heating	92
3.5 Model Updating of Curved Panel Subjected to Localized Central Heating	93
3.6 Effect of Uncertainty in the Panel Model Subjected to Localized Heating	94
4 Conclusion	95
References	96
On Affine Symbolic Regression Trees for the Solution of Functional Problems	97
1 Introduction	97
2 Symbolic Regression Is a Search Problem	98
3 Enumerating Search Spaces	99
4 Affine Regression Trees	103
5 Illustration with a Benchmark Set	106
6 Conclusions	108
References	109
Comparative Analysis of Mechanical and Magnetic Amplitude Stoppers in an Energy Harvesting Absorber	111
1 Introduction	111
2 Nonlinear Reduced-Order Modeling	111
3 Analysis	112
4 Conclusions	113
References	114
NIXO-Based Identification of the Dominant Terms in a Nonlinear Equation of Motion	115
1 Definition of the -Indicators	115
2 Simulated Black-Box Identification of a Curved Beam	116
3 Identification of Mode 1	116
4 Sample Black-Box ID Outcomes from High-Amplitude Vibration Tests	116
5 Validation of Results	118
6 Conclusion and Future Work	118
Reference	119
Nonlinear Dynamics and Characterization of Beam-Based Systems with Contact/Impact Boundaries	120
1 Introduction	120
2 Experimental Setup and Testing	121
3 Nonlinear Analysis of Beam with Hard Stoppers	121
4 Conclusions	123
References	123
Experimental Modal Analysis of Geometrically Nonlinear Structures by Using Response-Controlled Stepped-Sine Testing	124
1 Introduction	124
2 Nonlinear Experimental Modal Analysis with RCT and HFS	125
3 Experiment	126
4 Discussions and Conclusions	134
References	135
On the Application of the Generating Series for Nonlinear Systems with Polynomial Stiffness	136
1 Introduction	136
2 Background Theory and Definitions	137
2.1 Algebraic Structure	137
2.2 Iterated Integrals	138
2.3 Volterra Series	139
3 The Consolidated Expansion and a Diagrammatic Representation	139
3.1 Developing the Diagrammatic Representation	140
4 Generating Series for the Asymmetric Duffing Oscillator	141
4.1 Shuffle Product of Series Terms	144
4.2 The Asymmetric Duffing Oscillator	144
5 Determining System Response	146
6 Response to Gaussian White Noise	147
7 Conclusions	149
References	149
A Hybrid Static and Dynamic Model Updating Technique for Structures Exhibiting Geometric Nonlinearity	151
1 Introduction	151
2 Hybrid Testing: Theory	152
3 Static Test and Stiffness Updating	152
4 Nonlinear Static Test and Model Updating	153
5 Dynamic Test and Mass Updating	154
6 Test Setup and Finite Element Modeling	155
7 Results	156
8 Conclusion and Future Scope	157
Appendix	159
References	160
Insights on the Dynamical Responses of Additively Manufactured Systems	162
1 Introduction	162
2 Additively Manufactured Beams and Experimental Setup	163
3 Filament Orientation Effects on the Linear Characteristics of PLA-Beam Systems	163
4 Conclusions	164
References	165
Characterization of Nonlinearities in a Structure Using Nonlinear Modal Testing Methods	166
1 Introduction	166
2 Theoretical Background	167
3 Phase-Locked Loop	168
4 Software Phase-Locked Loop	168
5 Test Rig Details	170
6 Results	171
7 Conclusion and Future Work	176
References	176
Challenges of Characterizing Geometric Nonlinearity of a Double-Clamped Thin Beam Using Nonlinear Modal Testing Methods	178
1 Introduction	178
2 Theoretical Background	179
3 Phase-Locked Loop: Theory and Implementation	180
4 Test Structure and Instrumentation Details	182
5 Results	182
6 Conclusion and Future Work	185
References	186
Establishing the Exact Relation Between Conservative Backbone Curves and Frequency Responses via Energy Balance	188
1 Introduction	188
2 Prediction of Forced-Damped Responses from the Conservative Limit	189
3 Conclusion	190
References	191
Joint Interface Contact Area Predictions Using Surface Strain Measurements	192
1 Introduction	192
2 Experimental Specimen	192
3 Results	193
Reference	194
Towards Compact Structural Bases for Coupled Structural-Thermal Nonlinear Reduced Order Modeling	195
1 Introduction	195
2 Coupled Structural-Thermal NLROM	196
3 Enrichment for Two-Temperature-Field Scenario	198
4 Methods for Construction of Compact Enriched Bases	199
4.1 Method of Progressive POD	199
4.2 Method of Static Condensation	201
5 Comparison of Three Enriched ROMs with Nastran	203
6 Conclusions	204
References	204
Ensemble of Multi-time Resolution Recurrent Neural Networks for Enhanced Feature Extraction in High-Rate Time Series	205
1 Introduction	205
2 Algorithm Architecture	206
3 Simulations on Drop Tower Data	206
4 Conclusion	207
References	208
Modelling the Effect of Preload in a Lap-Joint by Altering Thin-Layer Material Properties	209
1 Introduction	209
2 Experimental Analysis of Lap-Joint	210
3 The Modified Thin-Layer Approach	211
4 3D Detailed Model	212
5 2D Equivalent Model	213
6 Conclusion	215
References	215

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