Advanced Problem in Mechanics II: Proceedings of the XLVIII International Summer School-Conference “Advanced Problems in Mechanics”, 2020, St. ... (Lecture Notes in Mechanical Engineering)

This book focuses on original theories and approaches in the field of mechanics. It reports on both theoretical and applied researches, with a special emphasis on problems and solutions at the interfaces of mechanics and other research areas. The respective chapters highlight cutting-edge works fostering development in fields such as micro- and nanomechanics, material science, physics of solid states, molecular physics, astrophysics, and many others. Special attention has been given to outstanding research conducted by young scientists from all over the world. This book is based on the 48th edition of the international conference “Advanced Problems in Mechanics”, which was held in 2020, in St. Petersburg, Russia, and co-organized by The Peter the Great St. Petersburg Polytechnic University and the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, under the patronage of the Russian Academy of Sciences. It provides researchers and graduate students with an extensive overview of the latest research and a source of inspiration for future developments and collaborations in mechanics and related fields. Preface Organization Scientific Committee Organizing Committee Minisymposia MS1 “Mathematical Modeling in Petroleum Engineering” Sec5 MS2 “New Approaches for Oil and Gas Reservoirs Simulation” Sec7 MS3 “Geometry, Topology, Fractal and Multifractal Modeling in Geosciences” Organizer MS4 “Extreme Loading on Structures” Sec11 MS5 “Nonlinear Waves in Continuous Media” Sec13 MS6 “Earthquakes and Seismic Protection” Sec15 MS7 “Scientific and Technical Creativity in Experimental Mechanics” Sec17 MS8 “Contact Mechanics, Tribology and Technology” Sec19 MS9 “Heat/Energy Transport in Discrete Systems” Sec21 MS10 “Sustainability of the Oil and Gas Industry: Challenges and Opportunities” Sec23 Contents Preface Organization Scientific Committee Organizing Committee Minisymposia MS1 “Mathematical Modeling in Petroleum Engineering” Sec5 MS2 “New Approaches for Oil and Gas Reservoirs Simulation” Sec7 MS3 “Geometry, Topology, Fractal and Multifractal Modeling in Geosciences” Organizer MS4 “Extreme Loading on Structures” Sec11 MS5 “Nonlinear Waves in Continuous Media” Sec13 MS6 “Earthquakes and Seismic Protection” Sec15 MS7 “Scientific and Technical Creativity in Experimental Mechanics” Sec17 MS8 “Contact Mechanics, Tribology and Technology” Sec19 MS9 “Heat/Energy Transport in Discrete Systems” Sec21 MS10 “Sustainability of the Oil and Gas Industry: Challenges and Opportunities” Sec23 Contents Plenary Lecture Poly-dispersed Droplets in Streaming Flows: Atomization, Evaporation, Combustion 1 Mathematical Model 2 Results of Numerical Investigations 3 Conclusions References Fluid Mechanics Viscoplastic Fluid Flow in a T-shaped Channel Under Given Pressure Boundary Conditions 1 Introduction 2 Problem Formulation 3 Numerical Method and Verification 4 Results and Discussion 5 Conclusion References Mathematical Modeling of the Flow of Viscous Incompressible Fluid with Suspended Particles in Flat Inclined Channel 1 Introduction 2 Numerical Research 2.1 Problem Statement 2.2 Mathematical Model 3 Results 4 Conclusion References Heat Transfer and Wave Motion Solitary Waves in Hyperelastic Tubes Conveying Inviscid and Viscous Fluid 1 Introduction 2 Equations of Motion of an Elastic Tube Containing a Flowing Viscous Fluid 2.1 Formulation of the Problem and Preliminary Relationships 2.2 Equations of the Tube Motion 2.3 Equations of Fluid Motion 2.4 Expression for Viscous Friction 2.5 Closed System of Equations 3 Steady-State Equations 3.1 Integration of the Fluid Equations 3.2 First Integrals of the Tube Equations 3.3 Non-dimensionalisation and Transition to Variables 1 and 2 3.4 Phase Plane 4 Steady States in the Case of an Inviscid Fluid 4.1 Phase-Plane Structure 4.2 Material Model 4.3 Phase Plane and Solitary Wave Solutions in the Case of a Quiescent Fluid 4.4 Phase Plane and Solitary Waves in the Case of a Moving Fluid 5 Steady States in the Case of a Viscous Fluid 5.1 Stretch Limit States as x 5.2 Evolution of the Tube When Moving from Infinity 5.3 Connection of Integral Trajectories from Infinities in the Central Part of the Tube 5.4 An Example of a Solution for an Infinitely Long Tube 5.5 Existence of Solitary-Wave-Like Solutions 6 Conclusions References A Note on the Propagation of Antiplane Love Waves in Micro-structured Media 1 Introduction 2 Problem Statement and Couple Stress Theory 2.1 Governing Equations 2.2 Assumption of Antiplane Shear Deformations 2.3 Assumption of Time-Harmonic Solution 2.4 Boundary and Interface Conditions 3 Love Waves Propagating in Micro-structured Media with Different Material Properties 3.1 Dispersion Equation 4 Results and Discussion 5 Conclusions and Open Issues References Acoustic Control of Cracks Self-healing in Plates: An Impulse Induced Wave Field in a Plate with an Initially Closed Crack Parallel to Its Free Surfaces 1 Introduction 2 Problem Formulation 3 Governing Equations 4 Problem Parameterization and Dimensional Analysis 5 Numerical Models 6 Simulation Results and Their Analysis 7 Discussion and Conclusion References Simulation of the Operation of a Detonation Engine 1 Introduction 2 Mathematical Model 3 Numerical Scheme 4 Kinetic Mechanism 5 Setting a Model Problem 6 Results 7 Postprocessing in High Definition Visualization System 8 Conclusions References Reduced Order Modeling for Thermo – Electric Processes 1 Introduction 2 Research of Thermoelectric Processes 3 Mathematical Model 3.1 Problem Formulation 3.2 Finite Element Formulation 4 Construct of Reduced Order Models of Thermoelectric System 4.1 Finite Element Model 4.2 Reduced Order Modeling in Matlab 5 Results 6 Conclusion References Experimental and Numerical Study of the Water-in-Oil Emulsion Thermal Motion in Rectangular Cavity with a Heated Bottom 1 Introduction 2 Experimental Research 3 Mathematical Modeling 4 Conclusion References Nonlinear Thermal Elastic Diffusion Problems Applicable to Surface Modification 1 Introduction 2 Preliminary Details 3 Nonlinear Equations of the Theory of Thermal Elastic Diffusion 4 Applications of Nonlinear Theory of Thermoelastic Diffusion 5 Conclusion References Nano-, Micro- and Mesomechanics Models of Nanosystems and Methods of Their Investigation, Connected with Orthogonal Splines 1 Introduction 2 Models of Nanomechanics and Methods of Their Investigation 3 Conclusion References Model of a Micromechanical Accelerometer Based on the Phenomenon of Modal Localization 1 Introduction 2 Derivation of the Equations of Motion 3 Finding Static Deflections 4 Comparison of Equilibrium Diagrams for Two Models 5 Analysis of the Spectral Properties of the System 6 Conclusions References Phase Transitions and Nonlinear Elasticity Reducing of Residual Stresses in Metal Parts Produced By SLM Additive Technology with Selective Induction Heating 1 Introduction 2 Growing Process 3 Initial-Boundary Problem at a Step 3.1 Skin Effect 3.2 Heat Transfer 3.3 Stress-Strain Problem 3.4 Eigenproblem 4 Computational Analysis and Discussion References Solids and Structures Critical Velocities and Stability of the Axially Moving Panels 1 Introduction 2 Basic Notions and Assumptions 3 Critical Velocities 4 Conclusion References Features of Applying HEDE Model to Description of the Destruction of Materials Induced by Hydrogen 1 Introduction 2 HEDE Model Review 3 Numerical Simulations 3.1 Statement of the Problem 3.2 Numerical Procedure 3.3 Model Parameters 3.4 Results of the Numerical Simulations 4 Discussion of the Results 5 Conclusions References Nonlinear and Multibody Dynamics, Chaos and Vibration Approximating Unstable Operation Speeds of Automatic Ball Balancers Based on Design Parameters 1 Introduction 2 Equations of Motion 2.1 Identification of the Viscous Drag Coefficient 3 Condition for Stable Balancing 4 Explicit Stability Border for the Isotropic Eccentricity Free Case 5 Conclusion and Outlook References Shape Control and Modal Control Strategies for Active Vibration Suppression of a Cantilever Beam 1 Introduction 2 Theoretical Background 2.1 Shape Control Method 2.2 Modal Control Method 3 The Control Problem 4 Creating the Control Systems: Actuator and Sensor Placement 4.1 Shape Control Method 4.2 Modal Control Method 5 Finite Element Modeling 6 Design of the Controller and Comparison of the Results 7 Conclusions References Axially Symmetric Oscillations of Circular Cylindrical Shell with Localized Mass on Winkler Foundation 1 Introduction 2 Statement of the Problem 3 Getting the View for the Vibration Field 4 Numerical Results 5 Conclusions References Mechanical and Civil Engineering Applications Statistical Quality Analysis of Bag-in-Box Packaging for Food Products 1 Introduction 1.1 Barrier Layer EVOH 1.2 Barrier Layer MetPET 1.3 Quality Control of the Bag 2 Statistical Analysis Methods 2.1 Histogram 2.2 The Differential Method (Quality Cobweb) 2.3 Horizontal histograms 2.4 Desirability Function 3 Results 3.1 Histograms 3.2 Quality Cobweb 3.3 Horizontal Histogram 3.4 Desirability Function 4 Conclusion References Modeling the Air Mixture Flow in an AC Plasma Torch 1 Introduction 2 Numerical Model 2.1 Basic Equations and Modeling Assumptions 2.2 Geometry and Boundary Conditions 3 Results and Discussion 3.1 Process Features 3.2 Reacting Mixture Model 4 Conclusion References Theoretical Basis of the Mechanism of Synchronous Rotation in Reverse Phase 1 Introduction 2 Background and Related Work 3 New Design of the Gas Distribution Mechanism 4 Mechanism of Synchronous Rotation in Reverse Phase. 5 Conclusion References Acoustoelastic Effect During Plastic Deformation of Anisotropic Metals 1 Introduction 2 Experimental Studies 3 Discussion 4 Conclusions References Minisymposium “Contact Mechanics, Tribology and Technology” Wear of Composite Materials in Full Contact with a Viscoelastic Body. The Steady-State Solution 1 Introduction 2 The Problem Formulation 3 Constitutive Equations for the Viscoelastic Body 4 The Solution for the Steady-State Regime 5 Results and Discussion 6 Conclusions References Pressure Concentration in 2D Elastic Regular Rough Contacts: The Effect of Asperity Interaction 1 Introduction 2 Contact Problems for 2D Sinusoidal Geometry with Different Type of Interaction 2.1 Periodic Contact Problem 2.2 Contact of a Single Sinusoidal Asperity with an Elastic Half-Plane 2.3 Contact of Two Single Sinusoidal Asperities with an Elastic Half-Plane 3 Results and Discussion 4 Conclusion References Effect of Friction in Sliding Contact of Layered Viscoelastic Solids 1 Introduction 2 Problem Formulation 3 Method of Solution 4 Results 5 Conclusions References The Simulation the Contact Interaction of the Needle and Brain Tissue 1 Introduction 2 The First Problem 3 The Second Problem 4 The Third Problem 5 The Forth Problem 6 Conclusion References Modeling of Fatigue Wear in Rolling Contact of Elastic Bodies 1 Introduction 2 Problem Formulation 3 Method of Solution 3.1 Shear Stresses Calculation 3.2 Damage Accumulation Model 4 Results and Discussion 4.1 Influence of Longitudinal Slip Velocity 4.2 Influence of Lateral Slip Velocity 4.3 Influence of Angular Velocity of Spinning 5 Conclusion References Minisymposium “Scientific and Technical Creativity in Experimental Mechanics” Dynamics of Hollow Cylindrical Magnets 1 Introduction and Problem Statement 2 Magnetic Field and Transformations 3 Total Force Analysis 3.1 Magnetic Interaction 3.2 Electric Interaction 4 Equation of Motion and Numerical Analysis 5 Results 5.1 Double Magnet Oscillator 5.2 Falling Magnet 5.3 Damped Magnetic Oscillator 6 Conclusion and outlook References Experimental Study on Hydraulically-Driven Fracture Initialization and Propagation in the Gelatin Mixture 1 Introduction 2 The Experimental Installation 3 The Experiment and Discussion 4 The Results of the Experiment 5 Mathematical Modelling 6 The Calculation Results 7 Conclusion References Correlation Model of Fracturing Fluid Viscosity with Regard to Proppant Concentration 1 Introduction 2 Experimental Setup 3 Experimental Procedure 4 Results 5 Discussion of Result 6 Conclusion References Minisymposium “Nonlinear Waves in Continuous Media” Solution of Equations for Plane Deformation of Nonlinear Model of Complex Crystal Lattice 1 Introduction 2 Nonlinear Model of Plane Deformation 3 Mathematical Methods of Implementation for Nonlinear Model of Plane Deformation 3.1 Solution of Macrofield Equations 4 Solutions of Microfield Equations 5 Modified Lamb Method of Solving Sine-Gordon Equation 5.1 Solution of Sine-Gordon Equation with Variable Amplitude 6 Conclusion References Solitary Acoustic Pulses Propagating at the Tip of an Elastic Wedge 1 Introduction 2 Theory 3 Results 4 Conclusions References Minisymposium “Extreme Loading on Structures” Free Vibrations of Thin Elastic Orthotropic Cantilever Cylindrical Panel 1 Introduction 2 The Statement of the Problem and the Basic Equations 3 The Derivation and Analysis of the Characteristic Equations 4 Planar Vibrations of an Orthotropic Cantilever Rectangular Plate 5 Bending Vibrations of an Orthotropic Cantilever Rectangular Plate 6 Asymptotics of Dispersion Eq. (24) 6.1 Asymptotics of Dispersion Eq. (24) at m 0 6.2 Asymptotics of Dispersion Eq. (24) at m l 7 Numerical Results 8 Conclusion Appendix References Stoneley Waves in Media with Microstructure 1 Introduction 2 Mechanical Framework for Antiplane Stoneley Waves 2.1 Constitutive Equations 2.2 Equations of Motion 2.3 Antiplane Shear Deformations 2.4 Reduced Force and Couple Stress Traction Vectors 2.5 Nondimensional Form of the Governing Equations 3 Analysis in the Frequency Domain 3.1 Waves Localized at the Half-Spaces' Interface 3.2 Dispersion Relation for Stoneley Waves 3.3 Cuton Frequency for Antiplane Stoneley Waves 4 Dispersion Curves 5 Conclusions 5.1 Funding References Assessment of the Behaviour of Low-Modulus Polyurethane Foams Subjected to Severe Shear Deformation Conditions 1 Introduction 2 Materials and Methods 2.1 Polyurethane Foam 2.2 The Shear Testing Machine 2.3 Specimen Preparation and Test Set-Up 2.4 Microstructure Analysis 3 Results and Discussion 3.1 Monotonic Shear Tests 3.2 Cyclic Shear Tests 4 Conclusions and Further Research Insights References Minisymposium “Earthquakes and Seismic Protection” Numerical Methods of Structures Seismic Analysis 1 Introduction 2 Response Spectrum Method Verification 2.1 Problem Statement 2.2 Results of Calculations 3 Direct Spectra-To-Spectra Method 3.1 Sorin Spectra-To-Spectra Method Description 3.2 Test Problem Description 3.3 Results of Calculations 4 Conclusion References Minisymposium “New Approaches for Oil and Gas Reservoirs Simulation” Modeling of Liquid Displacement from the Porous Medium Taking into Account the Presence of Hydraulic Fracture 1 Introduction 2 Mathematical Model 3 Results 3.1 Hydraulic Fracture Cleaning 3.2 Unstable Displacement of Oil by Water, Taking into Account the Presence of a Hydraulic Fracture 4 Conclusions References Application of a* Algorithm for Tortuosity and Effective Porosity Estimation of 2D Rock Images 1 Introduction 2 Methodology Description 2.1 Geometrical Path Calculation 2.2 Hydraulic Path Calculation 2.3 Characterization of Pore Structure 3 Case Study: 2D Image of Berea Sandstone 3.1 Results and Discussion 4 Conclusions References Minisymposium “Geometry, Topology, Fractal and Multifractal Modeling in Geosciences” Representative Elementary Volume via Averaged Scalar Minkowski Functionals 1 Introduction 2 The Scalar Minkowski Functionals 3 Evaluation of REV References The Fractal Model of Fractured Reservoirs Based on Pareto Distribution and Integrated Investigations 1 Introduction 2 Distribution Daily and Cumulative Production in Wells at the Different Fields 2.1 Physical and Mathematical Modeling 2.2 The Generator of Power Law Distribution and Pareto Law 3 The Fractal Model of Fractured Reservoirs 4 Conclusion References Multifractal Interpretation of Images of Coal Specimen Surfaces to Assess the Degree of Coal Tectonic Disturbance 1 Introduction 2 Semimi 3 Source Data 4 Research Results References Author Index