Nonlinear Dynamics of Structures, Systems and Devices (Proceedings of the First International Nonlinear Dynamics Conference (NODYCON 2019), Volume I) ||

This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics. Preface Volume 1: Nonlinear Dynamics of Structures, Systems, and Devices Volume 2: Nonlinear Dynamics and Control Volume 3: New Trends in Nonlinear Dynamics Preface for Volume 1: Nonlinear Dynamics of Structures, Systems, and Devices Contents Contributors Part I Methods for Nonlinear Dynamics Nonlinear Dynamics of Multibody Systems Using an Augmented Lagrangian Formulation 1 Introduction 2 Equations of Motion: Augmented Lagrangian Formulation 3 Numerical Results 3.1 Planar Slider-Crank Mechanism 3.2 Complex Model of a Ground Vehicle References Stability Boundary Approximation of Periodic Dynamics 1 Introduction 2 Statement of the Problem 3 Averaging Scheme 4 Monodromy Matrix Approximation 5 Stability Conditions in 2-Dimensional Case 6 Two DOF System with Impulse Parametric Excitation 6.1 High Frequency Stabilization of Inverted Pendulum 6.2 Exact Stability Conditions 6.3 Approximate Stability Conditions 7 Conclusion References 2-Order Normal Form Analysis for a Two-Degree-of-Freedom Nonlinear Coupled Oscillator 1 Introduction 2 2-Order Normal Form Analysis 3 Numerical Results 4 Conclusions References Vibrational Mechanics of Systems with Amplitude and Phase Modulation of Excitation 1 Introduction 2 Vibrational Forces for a System with Amplitude and Phase Modulation 2.1 Formulation of Problem 2.2 The Formula for Vibrational Force 2.3 Analysis and Main Regularities 2.4 Example 3 Conclusions References Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions 1 Introduction 2 Auxiliary Enzyme Reactions—Theoretical Framework 3 Numerical Results and Conclusion References A Novel Two-Stage Ellipsoid Filtering Based System Modeling Algorithm for a Hammerstein Nonlinear Model with an Unknown Noise Term 1 Introduction 2 Problem Statement 3 The Ellipsoid Volume Minimization Based Filtering Algorithm 4 Example 5 Conclusions References A New Method for the Frequency Response Curve and Its Unstable Region of a Strongly Nonlinear Oscillator 1 Introduction 2 Parameter-Splitting-Multiple-Scales Method 2.1 Parameter Splitting 2.2 The Solution to the Split System by the MS Method 2.2.1 Frequency Response Curve 2.2.2 Unstable Region 2.2.3 Approximate Response 2.2.4 Determination of Split Parameters 3 Illustrative Examples 4 Conclusions References Matrix Soliton Solutions of the Modified Korteweg–de Vries Equation 1 Introduction 2 Non-commutative Potential KdV, KdVand Modified KdV Hierarchies 3 Matrix Soliton Solutions 3.1 Operator Method 3.2 Soliton Solutions of mKdV Matrix Equation 3.3 Some Explicit Solutions of the Matrix Modified KdV Equation 4 Concluding Remarks References Part II Bifurcations and Nonsmooth Systems Bifurcations of Limit Directions at Codimension-2 Discontinuities of Vector Fields 1 Introduction 2 Extended Filippov Systems 2.1 Definition of Extended Filippov Systems 2.2 Limit Directions 2.3 Types of Limit Directions 3 Analysis of the Associated Smooth System 3.1 The Associated Smooth System in Polar Coordinates 3.2 Equilibrium Points and Bifurcations 4 Bifurcations of the Limit Directions 4.1 Relation Between the Associated System and the Original System 4.2 Tangency Bifurcation 4.3 Fold of Limit Directions 5 Conclusion References Boundary Layer Dynamics of Multibody Systems Involving Impact and Friction 1 Introduction 2 Mechanical Systems with a Single Frictionless Impact 3 Addition of Bilateral Constraints and Friction Effects 4 Numerical Results References Creation of Neimark-Sacker Bifurcation for a Three-Degree-of-Freedom Vibro-Impact System with Clearances 1 Introduction 2 Vibro-Impact System Under Impulsive StateFeedback Control 3 Creation of a Stable Neimark-Sacker Bifurcation 3.1 Design of Linear Control Gains for the Existence of Neimark-Sacker Bifurcation 3.2 Design of Nonlinear Control Gains for Stabilizing Neimark-Sacker Bifurcation 3.3 Nonlinear Control Gains Chosen for Adjusting the Amplitude of the Creating Invariant Cycle 4 Numerical Experiments 5 Conclusion References Analogue Models of Rocking Suitcases and Snaking Trailers 1 Introduction 2 Mechanical Model of Snaking Trailers 3 Linear Stability Analysis 3.1 The Pitch Motion of the Trailer 3.2 The Yaw and Roll Motion of the Trailer 4 Simulation 5 Conclusions References A Theoretical Model for Vibro-Impact Dynamics of Spur Gears with Tooth Flanks Wear 1 Introduction 2 A Mechanism of Mild Wear at Gears Tooth Flanks 3 A Vibro-Impact Model of Spur Gears with Tooth Flanks Wear 3.1 The Analytical Procedure Description 3.2 The Angular Velocities Variation During Vibro-Impact 4 Results and Discussion: A Case Study 4.1 Determination of Input Parameters 4.2 Results for Vibro-Impact Oscillations 5 Conclusions References Stability of Coupled and Damped Mathieu Equations Utilizing Symplectic Properties 1 Introduction 2 Floquet Theory Review 3 μ-Symplectic and γ-Hamiltonian Matrices 4 Linear γ-Hamiltonian Systems 4.1 Periodic γ-Hamiltonian Systems 5 Coupled Mathieu Equations with Damping 6 Conclusions References Asymmetry in the Basin Stability of Oscillation Death States Under Variation of Environment-Oscillator Links 1 Introduction 2 Coupling via Common Environment 3 Fractionally Disconnected Links 4 Discussion References The Occurrence of Zero-Hopf Bifurcation in a Generalized Sprott A System 1 Introduction 2 Invariant Spheres of Generalized Sprott A System 3 Zero-Hopf Bifurcation via Averaging Theory 3.1 Averaging Theory of First Order 3.2 Existence of a Periodic Orbit 4 Existence of Nested Invariant Tori 5 Concluding Remarks References Part III Nonlinear Phenomena in Mechanical Systems and Structures External and Internal Resonances in a Mass-Spring-Damper System with 3-dof 1 Introduction 2 Description of the Problem 3 Mathematical Model 4 Approximate Analytical Solution 5 External Resonance 6 Internal Resonance 7 Concluding Remarks References Internal Resonances in an Imperfect Circular Cylindrical Panel 1 Theoretical Formulation 2 Numerical Results 3 Concluding Remarks References Weakly Nonlinear Liquid Sloshing: Modelling and Exploration of Response Regimes 1 Introduction 2 Model Description 3 Dynamical Regimes 3.1 Periodic Responses 3.2 Weak Quasi-Periodic Responses 3.3 Strongly Modulated Responses (SMRs) 4 Numerical Results 5 Concluding Remarks References Catenary-Based Nonlinear Multimodal Theory of CableFree Vibrations 1 Introduction 2 Equations of Motion and Discretization 3 Multiple Scale Solution 4 Numerical Results 5 Conclusion References Flexural and Sway Interaction in the Nonlinear Vibrations of a Phenomenological Model of a Laterally Braced Column 1 Introduction 2 Formulation, Static Analysis, and Natural Frequencies 3 Nonlinear Dynamics Analysis 4 Conclusion References Influences of Temperature on Dynamic Behaviors of Suspended Cables Under Primary and Sub-Harmonic Excitations Simultaneously 1 Introduction 2 Mathematical Modeling 3 Perturbation Analysis 4 Numerical Examples and Discussions 5 Conclusions References Analysis of a Shape Memory Alloy Spring System Under Harmonic Excitation 1 Introduction 2 Mathematical Model 3 Numerical Simulation Method and Results 4 Conclusions References Vibration of Pre-Loaded Shallow Circular Arches 1 Introduction 2 Statics of Uniformly Loaded Shallow Arches 3 Small Vibration About Nonlinear Equilibria 4 Final Remarks References Nonlinear Vibration Responses of Laminated Composite Cantilever Plate in Subsonic Air Flow 1 Introduction 2 Derivation of the Subsonic Aerodynamic Force on the Flat Plate 3 Formulation 4 Conclusion References Adaptation of Energy Dissipation in a Laminated Module with Tunable Twin Wells 1 Introduction 2 Model Development 3 Approximate Approaches 3.1 Intrawell Oscillations 3.2 Interwell Oscillations 4 Frequency Response Curves and Dissipation Investigation 4.1 Excitation Frequency 4.2 Potential Function 5 Conclusion References The Duffing–Mathieu Equation Arising from Dynamics of Post-Buckled Beams 1 Introduction 2 The Mechanical Model and Equation of Motion 2.1 The Dimensionless Equation of Motion 2.2 The Galerkin Discretization and Duffing–Mathieu Equation 3 On the Stability Charts and a Bifurcation Diagram 4 Conclusions References Resonance-Induced Energy Localization in Weakly Dissipative Anharmonic Chains 1 Introduction 2 Equations of the Resonant Dynamics 3 Resonance in Non-dissipative Chains 4 Energy Localization in Weakly Dissipative Chains 5 Concluding Remarks References Part IV Experimental Dynamics, System Identification and Monitoring Torsional Analysis of Transmission Line Cables 1 Introduction 2 Material and Method 3 Results 4 Conclusions References Application of a Stochastic Version of the Restoring Force Surface Method to Identify a Duffing Oscillator 1 Introduction 2 Experimental Apparatus 3 Mechanical–Mathematical Modeling 4 Stochastic System Parameters Identification 5 Results and Discussion 6 Final Remarks References Modeling of the Hysteretic Behavior of Wire Rope Isolators Using a Novel Rate-Independent Model 1 Introduction 2 Proposed Hysteretic Model 2.1 PHM Formulation 2.1.1 Generalized Rate-Independent Force 2.1.2 History Variable 2.2 Parameter Sensitivity Analysis 3 Experimental Verification 3.1 Tested Wire Rope Isolator 3.2 Simulation of the Experimental Behavior 4 Conclusions References A Non-linear Model of Rubber Shear Springs Validatedby Experiments 1 Introduction 2 Model Development 2.1 Elastic Model 2.2 Friction Model 2.3 Viscous Model 3 Experimental Cyclic Tests of Shear Rubber Springs 4 Results and Discussion 5 Conclusion References Operational Modal Analysis on a Six-Degree-of-Freedom Parallel Manipulator: Reproducibility, Excitation and Pose Dependency 1 Introduction 2 Experimental Setup 3 Results and Discussion 3.1 Reproducibility 3.2 Shaker Reorientation and Relocation 3.3 Pose Dependency 4 Conclusion References Shaking Table Investigation on the Masonry Structures Behaviour to Earthquakes with Strong Vertical Component 1 Introduction 2 Description of the Experimental Tests 2.1 Tested Masonry Building Model 2.2 Experimental Setup 2.3 Experimental Results 3 Simplified Rocking Model 4 Conclusions References Quantifying Rate-Dependence of a Nonlinear Hysteretic Device 1 Introduction 2 Test Apparatus and Experimental Campaign 2.1 Results of Group A and Group B Tests 2.2 Results of Group C 2.3 Results of Group D 3 Rate-Dependence Matrices 4 Conclusions References Application of Photoelasticity to Some Nonlinear Dynamic Problems and Stress State Analysis in Dams: A Brief Overview Inspired by the Results of Prof. Vlatko Brčić 1 Introduction 2 Photoelasticity: Development and Dam Testing Applications 2.1 Invention and Early Development of Photoelasticity 2.2 Static Photoelastic Analysis of Dams and Prof. Brčić's Contribution 2.3 Improvements of the Method and Its Contemporary State 3 Contemporary Use of Photoelasticity in Nonlinear Dynamics 4 Concluding Remarks References Part V Fluid–Structure Interaction, Multibody System Dynamics Levitated and Parametrically Excited Sphere Dynamics in a Single-Axis Ultrasonic Levitator 1 Introduction 2 Derivation of the Governing Equations of Motion 3 Approximate Analytical Solution 4 Numerical Simulation Verification 5 Preliminary Experimental Results 6 Summary and Conclusions References Modelling VIV of Transversally Oscillating Rigid Structures Using Nonlinear Fluid Oscillators 1 Introduction 2 Mathematical Model: Modification and Calibration 3 Results and Discussion 4 Conclusions References Asymptotic Analysis of a Dynamical System for Vortex-Induced Vibration and Galloping 1 Introduction 2 Wake-Oscillator Model 3 Asymptotic Analysis 4 Discussion of Results 5 Concluding Remarks References A Quasi-Steady 3-DoFs Sectional Aerodynamic Model: Preliminary Results 1 Introduction 2 Aeroelastic Model 3 Stability Conditions 4 Application to a Full-Scale Dry Inclined/Yawed Cable 5 Conclusions References Lie Group Dynamics of Multibody System in Vortical Fluid Flow 1 Introduction 2 Multibody System Dynamics in Fluid Flow 3 Boundary Element Method 4 Point Vortices 5 Conclusions References Damping Models in Aircraft Flutter Analyses 1 Introduction 2 Theoretical Issues on Linear Viscoelastic Models and Their Performances 3 Aeroviscoelastic Model 4 Results 5 Concluding Remarks References Dynamic Response of a Morphing Wing 1 Introduction 2 Problem Formulation 3 Numerical Results 4 Conclusions References Helicopter Pilot Biomechanics by Multibody Analysis 1 Introduction and Motivation 2 Multibody Models 2.1 Upper Limb Model 2.2 Trunk Model 2.3 Models Parameterization 3 Examples 4 Conclusions References Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation 1 Introduction 2 Derivation of Non-dimensional Equation of Motion 2.1 Non-dimensional Mass Matrix 2.2 Non-dimensional Stiffness Matrix 2.3 Non-dimensional Force Vector 3 Numerical Solution of Non-dimensional Equation of Motion 4 Conclusions References Part VI Turning Processes, Rotating Systems, and Systems with Time Delays Approximated Dynamics of Chatter in Turning Processes 1 Motivation 2 Modelling and Analysis 2.1 Model Formulation 2.2 Stability 2.3 Bifurcation Analysis 3 Conclusion References Chaotic Dynamics in Spinning Shafts with Non-constant Rotating Speed Described by Variant Lyapunov Exponents 1 Introduction 2 Trajectories Around Equilibrium Manifolds 3 Numerical Results and Discussion 4 Conclusions 5 Acknowledgments References Post-Resonance Backward Whirl in a Jeffcott Rotor with a Breathing Crack Model 1 Introduction 2 Mathematical Model 2.1 Jeffcott Rotor Model 2.2 Numerical Simulation Results 3 Conclusions References Proper and Smooth Orthogonal Decompositions for Detection of Inner Race Defects in Rolling Element Bearings with Variable Rotational Speeds 1 Introduction 2 Experimental Setup and Data Collection 3 Diagnostic Method 3.1 Proper Orthogonal Decomposition 3.2 Smooth Orthogonal Decomposition 3.3 Feature Extraction and Supervised Learning 4 Fault Detection Results 5 Conclusions References Effect of the Compliance of the Part on the Double-Turning Process 1 Introduction 2 Design Scheme and Dynamic Models 3 Analysis of the Calculation Results 4 Conclusion References Effect of the Regenerative and Frictional Force on Chatter in Turning Process 1 Introduction 2 Model 3 Effect of the Regenerative Force and Frictional Force 4 Conclusions References Noise-Induced Transitions and Resonances in a Delayed Triple-Well Potential System 1 Introduction 2 Noise-Induced Transition 3 Noise-Induced Resonance 4 Conclusions References Application of the Second Dimension Reduction Method in Nonlinear Rotor Dynamic System 1 Introduction 2 Finite Element Model of Dual Rotor-Bearing System 3 First Dimension Reduction for Dual Rotor-Bearing System 4 Second Dimension Reduction for Dual Rotor-Bearing System 5 Results and Discussions Appendix References Vibration Analysis of Washing Machines in the Drum Plane 1 Introduction 2 Mathematical Modeling 3 Results and Discussion 4 Conclusion References Nonlinear Model for Wear Effects in Hydrodynamic Bearings Applied to Rotating Systems 1 Introduction 2 Numerical Model 3 Results and Discussion 4 Conclusions References Author Index Subject Index