Advances in Nonlinear Dynamics, Volume I

Name: Advances in Nonlinear Dynamics, Volume I | Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023)
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Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023)

Walter Lacarbonara(Editor)

Springer (Publisher)

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Published on 11. May 2024

XVI, 750 pages

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Content

Intro
Preface
Preface for Volume 1: Nonlinear Dynamics of Structures, Systems and Devices
Contents
Part I Fluid-Structure Interactions
Linear Stability of Thin Liquid Film Flows over a Uniformly Heated Slippery Substrate under Heat Flux Boundary Condition
1 Introduction
2 Formulation of the Problem
2.1 Governing Equations and Boundary Conditions
2.2 Scaling and Non-Dimensionalization
3 Boundary Layer Equations and Their Solutions
3.1 Asymptotic Expansions of Governing Equations and Boundary Conditions
4 Stability Analysis Using Infinitesimal Disturbance of the Basic Flow
4.1 Linear Stability Analysis Using Normal Mode of Disturbance
4.2 Results and Discussion
5 Weakly Nonlinear Models
6 Numerical Simulation
7 Conclusions
References
Linear Sheared Flow Effects in Vortex-Induced Forces on Three Tandem Subsea Structures in Proximity to Larger Objects
1 Introduction
2 Numerical Model
2.1 Mesh Verification
2.2 DES Model
2.3 Mesh Verification
3 Results and Discussion
4 Conclusions
References
Vortex-Induced Loads on Subsea Pipelines Due to Marine Biofouling
1 Introduction
2 Numerical Model
3 Results and Discussion
4 Conclusions
References
A New Koopman-Inspired Approach to Match Flow Field Excitation with Consequent Structure Responses for Nonlinear Fluid-Structure Interactions
1 Introduction
2 The Koopmanistic Approach
2.1 Theoretical Context
2.2 Approach to Solution
2.3 Solution Procedure
3 Results and Discussions
4 Conclusions
References
The Remarkable Role of Hydrogen in Conductors with Copper and Silver Nanoparticles by Mixed Convection Using Viscosity Reynold's Model
1 Introduction
2 Modeling and Formulation of the Problem Statement
3 Computational Methodology
4 Results and Discussions
5 Conclusions and Recommendations
References
Nonlinear Stability of a Thin Viscoelastic Film Down a Vertical Wall: A Numerical Study
1 Introduction
2 Problem Description
3 Nonlinear Dynamical Simulations
4 Role of Odd Viscosity
5 Summary and Conclusions
References
Dynamics of a Completely Immersed Nonlinear Beam Under the Action of a Sea Wave
1 Introduction
2 Modeling and Dynamic Analysis
2.1 Physical and Mathematical Modeling
2.2 Analytical Study
3 Results and Discussion
4 Conclusions
References
Semi-Analytic Solutions for the Bending-Bending-Torsion Coupled Forced Vibrations of a Rotating Wind Turbine Blade by Means of Green's Functions
1 Introduction
2 Governing Equations of Bending-Bending-Torsion Coupled Forced Vibrations of a Rotating Wind Turbine Blade
3 Green's Functions of the Bending-Bending-Torsion Forced Vibration Problem of a Rotating Wind Turbine Blade
3.1 Green's Functions for Eq. (8Equ55)
3.2 Green's Functions for Eqs. (8Equ33) and (8Equ44)
3.3 Boundary Conditions of a Rotating Wind Turbine Blade
4 Semi-Analytic Solutions for the Bending-Bending-Torsion Coupled Forced Vibrations of a Rotating Wind Turbine Blade
5 Numerical Results and Discussions
5.1 Verification of the Present Solutions
5.2 Effects of the Speed
6 Conclusions
Appendix 1
References
Part II Mechanical Systems and Structures
Multiple Periodic Symmetric Limit Cycles of Two Coupled Sommerfeld Rotors
1 Introduction to the Problem
2 Equations of Motion of the Sommerfeld Rotor
3 Equations of Motion in the Cauchy Form
4 Corrected Speed Driving Moment Characteristic
5 Airplane Wing Motor Model with Unbalanced Rotors
6 Cauchy Form of the Rotor System Equations
7 Periodic Limit Cycles Calculated by Time-Free Equations
8 Summary and Concluding Remarks
References
Multiharmonic Forced Response Analysis of a Torsional Vibration Isolator Using a Nonlinear Quasi-zero Stiffness Approach
1 Introduction
2 Modeling and Solving
2.1 Multiharmonic Equation of Motion
2.2 Continuation of Solution Branch
2.3 Evaluation of Nonlinear Torque
2.4 Validation of Simulation Procedure
3 Analysis of QZS Dynamics
3.1 Nonlinear Rotational Stiffness
3.2 Dynamics of QZS Isolator
3.2.1 Excitation Torque Amplitude exc,1
3.2.2 Damping d
3.2.3 Degree of Isolation ?
3.2.4 Static Offset ?fstat
3.3 Engine Application
4 Conclusions
References
Predicting Limit Cycle of Modified Rayleigh Differential Equation
1 Introduction
2 Problem Statement and Formulation
3 Results and Discussion
4 Conclusions
References
An Extensible Double Pendulum and Multiple Parametric Resonances
1 Introduction
2 The System
3 Numerical Investigation of Resonances
4 Discussion
References
A Perturbation Theory for the Shape of Central Force Orbits
1 Introduction
2 The Exact Solution to n=2 and n=-1 Cases
3 Perturbative Approach to Solve the Orbit Equation and Spatial Frequency
4 Theoretical Consistency
5 Closed or Space Filling?
6 Numerical Consistency
7 Conclusion
References
Analysis of Forced Vibrations of a Nonlinear Elastic Plate on a Viscoelastic Foundation Subjected to Hard Excitation from Harmonic Load
1 Introduction
2 Problem Formulation
3 Method of Solution
3.1 Nonresonant Hard Excitation
3.2 Superharmonic Resonance OF13?1
3.3 Subharmonic Resonance F 31
4 Numerical Results
5 Conclusions
References
Mathematical Modelling of a Coefficient of Nonlinearity in Dynamics of Deep Groove Ball Bearing with Damage
1 Introduction
2 Modelling of Deep Groove Ball Bearings with Damage
3 Mathematical Modelling of a Coefficient of Nonlinearity
3.1 Mathematical Modelling of Damaged Bearing Dynamics
3.2 Empirical Procedure
4 Discussion and Conclusions
References
Regular and Complex Behavior in the Pendulum System Under a Magnetic Field
1 Introduction
2 Basic Model
3 Investigation of the Localized Mode of the Pendulum System
3.1 The Study of the Localized Mode by the Multiple Scales Method
3.2 Investigation of the Influence of the System Parameters and Initial Conditions on the Localized Mode
4 Investigation of the Coupled Mode of the Pendulum System
4.1 Investigation of the Coupled Mode by the Multiple Scales Method
4.2 Investigation of the Influence of System Parameters and Initial Conditions on the Dynamics of the System (Coupled Mode Case)
5 Conclusions
References
Nonlinear Free Vibration of Functionally Graded Shallow Shells with Variable Thickness Resting on Elastic Foundation
1 Introduction
2 Formulation of the Problem
3 Solution Method
4 Numerical Results and Discussion
5 Conclusions
References
Nonlinear Free Vibrations of Functionally Graded Porous Sandwich Plates with Complex Shape
1 Introduction
2 Mathematical Formulation
3 Solution Method
4 Numerical Results
4.1 Test Problem. Simply Supported and Clamped Porous FGM Sandwich Plates with Rectangular Shape
4.2 Plates with a Complex Shape
5 Conclusion
References
Effect of Boundary Conditions on the Stability of a Viscoelastic Von Mises Truss
1 Introduction
2 Symmetric Boundary Conditions
2.1 Nondimensionalization
2.2 Stability Results
3 Asymmetric Boundary Conditions
3.1 Stability Results
4 Conclusion
References
Study of the Effect of Non-linear End Supports on the Unbalance Response of the Elastic Shaft
1 Introduction
2 Analysis
3 Results and Discussion
4 Conclusions
References
Influence of the Rope Sling System on the Dynamics of a Carried Load
1 Introduction
2 Dynamics Model
3 Numerical Calculation Results
4 Conclusions and Summary
References
Part III Computational Nonlinear Dynamics
Differential Formulation of the Vaiana-Rosati Model of Hysteresis: Preliminary Results
1 Introduction
2 VRM Analytical Formulation
3 VRM Differential Formulation
4 Simulation of Complex Hysteresis Loops
5 NLTHAs of a SDOF Hysteretic Mechanical System
5.1 Discrete Structural Model
5.2 Nonlinear Equilibrium Equation
5.3 Applied External Force
5.4 Hysteretic Model Parameters
5.5 NLTHAs Results
References
Modified Energy-Based Time Variational Methods for Obtaining Periodic and Quasi-Periodic Responses
1 Introduction
2 TVM Formulation
3 Modified TVM with Linear Domain Transformation
4 MTVM Formulation
5 TVEM Formulation
6 MTVEM Formulation
7 Conclusion
References
An Algebraic Model for Hysteretic Responses Exhibiting Cyclic Hardening and Softening Phenomena: Preliminary Results
1 Introduction
2 Algebraic Model
3 Evaluation of the Generalized Work
4 AM Experimental Validation
4.1 Tested Samples
4.2 AM Parameters Calibration Procedure
5 Conclusions
References
A General Co-simulation Framework Based on a Novel Weak Formulation at the Interface Level
1 Introduction
2 Introduction of the New Numerical Integration Scheme
2.1 Piecewise-Linear Polynomials
2.2 Piecewise-Quadratic Polynomials
3 Description of the Novel Co-simulation Strategy
3.1 Force/Displacement (F/D) Decomposition
3.1.1 Piecewise-Linear Polynomials
3.1.2 Piecewise-Quadratic Polynomials
4 Numerical Results and Discussion
4.1 Numerical Integration
4.2 Co-simulation
5 Synopsis and Future Work
References
Abstract Dynamics: An Alternative Approach to Local Lyapunov Exponents in Examining Local Unpredictability
1 Introduction
2 Methodology
2.1 Preliminaries
2.2 Overall Structure
3 Results
3.1 Simple Periodic Motion of a Limit Cycle: The Van der Pol Oscillator
3.2 Scrutinizing Abstract Dynamics by Chaos: The Lorenz Attractor
3.3 Chaotic or Nonchaotic, Periodic or Aperiodic
4 Conclusion
References
Energy Pumping of Mechanical Oscillators in an Array Configuration Under Impulse and Parametric Excitation
1 Introduction
2 Mathematical Model
3 Slow Flow Equations of Amplitude and Phase
4 Numerical Analysis
4.1 Energy Transfer Under Impulse Excitation
4.1.1 Variation in Energy Pumping Due to Frequency Detuning
4.1.2 Effect of NES Oscillator Model on Energy Transfer in Array Configuration
4.2 Energy Transfer in an Array Under Parametric Excitation
4.3 Two-Way Spatial Energy Transfer in a Closed Loop
5 Conclusions
References
On the Velocity-Based Description in Dynamic Analysis of Three-Dimensional Beams
1 Introduction
2 Cosserat Rod Model
2.1 Equations of Motion
2.2 Strain Measures
2.3 Angular Momentum Balance Equation in Local Frame
3 Numerical Solution
4 Energy Conservation
5 Numerical Examples
5.1 Free Flight of a Beam
5.2 Right-Angle Cantilever
5.3 Four-Bar Mechanism
6 Conclusion
References
Unconditionally Stable Time Stepping Scheme for Large Deformation Dynamics of Elastic Beams and Shells
1 Introduction
2 Large Deformation Dynamic Problem with General Nonlinear Strain Measure
2.1 One-Step Time Integration
2.2 The New Integration Scheme
2.3 Extension to Nonlinear Multi-body Coupling Laws
3 Numerical Examples
3.1 Cantilever Beam
3.2 Thin-Walled Cantilever Beam with Local Buckling
3.3 Tumbling Cylinder
4 Conclusion
References
Computing Periodic Responses of Geometrically Nonlinear Structures Modelled Using Lie Group Formulations
1 Introduction
2 Lie Group Beam Model
3 Periodic Solutions
4 Straight Clamped-Clamped Beam
4.1 NNM 2
5 Shallow Arch
5.1 NNM 1
5.2 NNM2
6 Conclusion
References
An Extensive Test Campaign of a Turbine Bladed Disk in the Presence of Mistuning and Underplatform Dampers, and Numerical Validation
1 Introduction
2 Experimental Campaign
3 Numerical Modeling
3.1 Model Order Reduction for Mistuned Bladed Disks
3.2 Frequency-Domain Analysis
4 Experimental-Numerical Validation
5 Conclusions
References
New Existence Results for Sequential Generalized Nonlinear Hilfer Fractional q-Differential Inclusions via Multi-point Boundary Conditions
1 Introduction
2 Basic Concepts and Preliminaries
2.1 Fractional Quantum Calculus
2.2 Set-Valued Analysis
3 Existence Results for Set-Valued Problems
3.1 The Upper Semi-continuous Case
3.2 The Lipschitz Case
4 Illustrative Examples
5 Conclusion
References
New Elemental Damping Model for Nonlinear Dynamic Response
1 Introduction
2 Existing Elemental Damping Model and Problems
3 Proposed Elemental Damping Model
4 Evaluation in Time History Analysis
5 Conclusions
References
Active Learning for Probabilistic Machine Learning-Based Modeling of Dynamical Systems
1 Introduction
2 Methods
2.1 Gaussian Processes
2.2 Active Learning
3 Experiments and Results
3.1 Data Generation
3.2 Experiments Setup
3.3 Results
4 Conclusion
References
Optimal Projection in a Koopman-Based Sorting-Free Hill Method
1 Introduction
2 Classical Floquet Theory for Smooth Systems
3 Koopman Lifting the LTV Dynamics
4 Monodromy Matrix and Stability
5 Projection Matrix Optimization
6 Application to a Vertically Excited Multiple Pendulum
7 Conclusion
References
Computation of the Wright Function from Its Integral Representation
1 Introduction
2 Applications
3 The Canonical Complex Integral Representation
4 Derivation of the Real Integral Representation
4.1 The Double-Exponential (DE) Quadrature Method
5 Numerical Results
5.1 Computation of the Mainardi's Wright Function and Its Integral
5.2 Computation of Gaussian Derivatives and Hypergeometric Functions
5.3 Computation of Bessel and Trigonometric Functions
6 Discussion
References
Numerical Modeling and Experimental Validation of Ballistic Panel Penetration
1 Introduction
2 Description of the Experimental Tests Carried Out on the Penetration of the Shield with the Use of an Armor-Piercing Projectile
2.1 Description of the Experimental Setup
2.2 Analysis of Results and Assessment of Measurement Errors
3 Validation Based on a Model of a Steel Target Subjected to a 7.62x54R B32 Projectile Test
3.1 Numerical Models
4 Verification Using a Variant Consisting of Two Targets (Ceramic/Steel) Subjected to a 7.62x54R B32 Bullet Test
4.1 Conclusions
References
Mean-Reverting Schemes for Solving the CIR Equation
1 Introduction
2 A New Family of Methods
3 Mean-Reverting Schemes
4 Long-Term Second Moment
5 Numerical Experiments
6 Conclusions
References
Implicit Milstein Schemes: Preservation of Properties When Solving the CIR Equation
1 Introduction
2 Preservation of Non-Negativity by ?-Milstein Methods
3 Mean-Reverting ?-Milstein Schemes
4 Long-Term Second Moment
5 Numerical Experiments
6 Conclusions
References
New Formula of Geometrically Exact Shell Element Undergoing Large Deformation and Finite Rotation
1 Introduction
2 Theory of Geometrically Exact Shell Element
2.1 Kinematics of Shell
2.2 Geometric Descriptions for Director Vector
2.3 Strain Analysis of Shell
2.4 Elastic Force of Shell
2.5 Variation of Kinetic Energy
2.6 Virtual Work of External Loads
2.7 Governing Equations of Motion
3 Numerical Examples
3.1 3D Cantilever Bend
3.2 Eigenmode Analysis of Horten IV Flying Wing
4 Conclusion
References
Estimating Seismic Behavior of Buckling-Restrained Braced Frames Using Machine Learning Algorithms
1 Introduction
2 Modeling of Structures
3 ML Method
4 Results
5 Conclusions
References
Part IV Analytical Techniques
Regularity and Spatially Distributed Solutions for Interacting Gases in Complex Domains
1 Introduction
2 Regularity and Global Behaviour of Solutions
3 Spatially Distributed Solutions
4 Conclusions
References
Nonlinear Effects of the Central Body Oblateness on the Coplanar Dynamics of Solar Sails
1 Introduction
2 Perturbation Model
3 Hamiltonian Approach
3.1 Short-Period Elimination
3.2 The Coplanar Manifold
4 Conclusions
References
Collinear Point Dynamics of a Dumbbell Satellite in Fast Rotation
1 Introduction
2 The Dumbbell Satellite in the Fast Rotation Model
3 Hamiltonian Normalization
4 Slow Dynamics on the Center Manifold
4.1 Regions of the Parameter Plane with a Different Flow
4.2 The Slow Flow on the Sphere
5 Conclusion
References
Modelization of Thermally Induced Jitter in an Orbiting Slender Structure
1 Introduction
2 Thermal Analysis
2.1 Steady-State Thermal Analysis
2.2 Transient Thermal Analysis
3 Nodal Analysis
3.1 Isothermal Analysis
3.2 Two-Node Analysis
3.3 Analytical Equation
3.4 Discussion
4 Conclusions
References
Introduction to the Perpetual Mechanics Theory: The Starting Point and Future Directions
1 Introduction
2 Modeling and Dynamic Analysis
3 Introduction of the Perpetual Mechanics Theory
3.1 Perpetual Points and the Dynamics of Unforced Mechanical Systems
3.2 Externally Forced Perpetual Mechanical Systems
3.3 Mechanical System's Motions Without Degradation, Energy Loss Leading to Perpetual Machines of the Third-Kind Behavior
3.4 Applications of the Perpetual Mechanics Theory
4 Numerical Simulations Validating the Theory
4.1 The Theory Applied to the PMS of the "Free" Configuration
4.2 The Theory Applied to the PMS of the "Embedded" Configuration
5 Conclusions and Discussion for Future Directions
References
Nonlinear Vibration Analysis of Specially Orthotropic Tapered Plate with Arbitrarily Oriented Crack: An Analytical Approach
1 Introduction
1.1 Governing Equation
1.2 Solution of Governing Equation
1.3 Specially Orthotropic Plate with Unidirectional Linearly Varying Thickness
1.4 Frequency Response
2 Results and Discussions
2.1 Validation of the Results
2.2 New Results
3 Conclusion
References
Modelling Thermoelastic Damping in Nonlinear Plates with Internal Resonance
1 Introduction
2 Governing Equations of Motion
3 Results and Discussion
3.1 Single-Mode Approximation
3.2 Two-Mode Approximation
4 Conclusion
References
Part V Bifurcation and Dynamic Instability
Nonlinear Dynamic Characteristics and Four Contact States of a Spur Gear Pair Considered Tooth Profile Error and Extended Tooth Contact
1 Introduction
2 The Dynamic Model of a Spur Gear Pair with Tooth Profile Error and Extended Tooth Contact
3 Five Poincaré Mapping Sections for Obtaining Nonlinear Behavior and Contact States of the System
4 Simulation Results and Discussion
5 Conclusion
References
Nonlinear Vibration of an Inextensible Rotating Beam
1 Introduction
2 Description of the Problem
3 Solution Procedure
4 Results and Discussion
5 Conclusion
References
A Complete Stability Chart for the Tippedisk
1 Introduction
2 Mechanical Model of the Tippedisk
3 Normalized Singularly Perturbed Dynamics
4 Local Stability Analysis on the Slow Manifold
4.1 Local Stability of Inverted Spinning
4.2 Local Stability of Non-inverted Spinning
5 Global Heteroclinic Bifurcation
6 The Big Picture
7 Discussion
8 Conclusion
References
The Interplay Between the Electro-Magnetic and Wave-Induced Instability Mechanisms in the Hyperloop Transportation System
1 Introduction
2 Model and Solution Method
2.1 Model Formulation
2.2 Solution Method
3 Linearisation of the Nonlinear Model
4 Results and Discussion
5 Conclusions
References
Part VI Rotating Systems
A Method for the Analysis of the Aeroelastic Stability of Slender Wind Turbines and Its Validation
1 Introduction
2 Methodology
2.1 General Linearization
2.2 Linearized Aeroelastic Dynamics
2.3 Coordinate Transformation
2.3.1 Corotational Formulation in the Floating Frame of Rotation Center
2.3.2 MBC Transformation
2.4 Modal Analysis
3 Validation
4 Conclusions
References
Parametric Resonances due to Torsional Oscillations of a Multi-degree of Freedom Driveline Coupled by a Series of Universal Joints
1 Introduction
2 Equations of Motion
3 Analytical Linear Stability Analysis
3.1 Linear Eigenvalue Analysis
3.2 Harmonic and Sub-harmonic Resonances
3.3 Combination-Type Resonances
4 Results and Discussions
4.1 Numerical Linear Analysis
4.2 Numerical Non-linear Analysis
5 Conclusion
6 Conflict of Interest
References
Part VII Nonsmooth Systems
Investigation on Vibro-Impacts of Electric Powertrain in Regenerative Braking Process
1 Introduction
2 Electromechanical Model of the Powertrain
3 Results and Discussion
4 Conclusions
References
Experimental Analysis of a Nonlinear Piecewise Multi-degrees-of-Freedom System
1 Introduction
2 Experimental Setup
3 Methodology and Data Acquisition
4 Nonlinear Experimental Results
5 Conclusion
References
Higher Order Transverse Discontinuity Mapping for Hybrid Dynamical Systems
1 Introduction
2 Non-smooth FSI System
3 Numerical Results
4 Conclusion
References
Part VIII Experimental Dynamics
Analysis of Nonlinear Vibrations Using DIC and the Smoothed Harmonics Method
1 Introduction
2 Down-Sampling Methods
2.1 Smoothed Harmonics Method
2.2 Sensitivity to Noise and Sampling Parameters
3 Forced Vibration of a Beam with Nonlinear Boundary Conditions
3.1 Numerical Simulation
3.2 Experimental Setup
4 Conclusion
References
Experimental and Numerical Study of a Magnetic Pendulum
1 Introduction
2 A Magnetic Pendulum
2.1 Experimental Set-Up
2.2 Mathematical Model
2.3 Non-dimensional Form
3 Equilibrium Points
4 Free Vibration Analysis
5 Conclusion
References
Effects of Controller-Induced Dynamics on Experimental Bifurcation Analysis
1 Introduction
2 Stalling Dynamics of Angle-Encoded Systems
2.1 Prototypical Stalling System
2.2 Mechanism of Stalling
3 Overcoming Stalling Dynamics
4 Discussion and Conclusion
References
Rail-Structure Interaction Parameters at Ballasted Viaduct in Rohtak-Gohana Elevated Stretch: Instrumentation, Measurements, and Interpretation
1 Introduction
2 Bridge-Track Description
3 Selected Spans for the RSI Study
4 Codes/Manuals Used for the Study
5 Data Acquisition System and Sensors
6 Determination of Displacement and Horizontal Support Reactions
7 Results and Discussion
8 Conclusions
References
A Laboratory-Scale Foucault Pendulum for the Measurement of Frame-Dragging
1 Introduction
1.1 The Modelling of Frame-Dragging in the Vicinity of the Earth by Means of Gravitoelectromagnetism, and the Challenges of a Terrestrial Measurement
2 A Laboratory-Scale Foucault Pendulum
3 Pendulum Tracking Analysis
4 Conclusions
References
Correction to: Abstract Dynamics: An Alternative Approach to Local Lyapunov Exponents in Examining Local Unpredictability
Correction to: Abstract Dynamics: An Alternative Approach to Local Lyapunov Exponents in Examining Local Unpredictability
Correction to:Chapter 26 in: W. Lacarbonara (ed.), Advances in Nonlinear Dynamics, Volume I, NODYCON Conference Proceedings Series, https://doi.org/10.1007/978-3-031-50631-4_26
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