Progress in Continuum Mechanics

TRAMA

This book gives an insight into the current developments in the field of continuum mechanics. Twenty-five researchers present new theoretical concepts, e.g., better inclusion of the microstructure in the models describing material behavior. At the same time, there are also more applications for the theories in engineering practice. In addition to new theoretical approaches in continuum mechanics and applications, the book puts an emphasis on discussing multi-physics problems.

SOMMARIO

1 A Semi-Empirical Fluid Force Model for Vortex-Induced Vibration of an Elastic Structure Andrei K. Abramian and Sergey A. Vakulenko1.1 Introduction 1.2 A Fluid Force Model 1.2.1 Formulation of the Problem 1.2.2 Solution of the Structure Motion Equation 1.2.2.1 Pure Resonance Case 1.2.2.2 Near Resonance Case 1.2.2.3 Non-Resonant Case 1.2.3 Effect of Variation of an Added Mass with the Reduced Velocity 1.3 An Example 1.4 Conclusion and Discussion References 2 Nonlinear Buckling and Equilibria of Layered Shallow Parabolic Arches with Interlayer Slip Christoph Adam, Ivan Paulmichl, and Thomas Furtmüller2.1 Introduction 2.2 Basic Equations 2.3 Solution 2.4 Buckling and Post-Buckling Analysis 2.4.1 Primary Equilibrium Path 2.4.2 Limit Loads and Limit Points 2.4.3 Bifurcation Loads and Bifurcation Points 2.4.4 Post-Bifurcation Equilibrium Path 2.5 Application 2.5.1 Example Problem 1 2.5.2 Example Problem 2 2.5.3 Critical Loads 2.5.4 Parabolic Shallow Arch vs. Circular Shallow Arch 2.6 Summary and Conclusions References 3 On the General Strategies to Formulate Shell and Plate Theories Holm Altenbach and Victor A. Eremeyev3.1 Introduction 3.2 Classification Principles 3.2.1 Classification of Structural Models 3.2.2 Classification of Theories for Two-Dimensional Structures 3.3 Direct Approach 3.3.1 General Cosserat Surface Theory 3.3.2 12-Parameter Theory 3.3.3 6-Parameter Theory 3.3.4 5-Parameter Theory 3.3.5 3-P arameter Theory 3.4 Conclusions References 4 Conceptual Generalizations of the Kapitsa Problem Alexey V. Babenko, Oksana R. Polyakova, and Tatyana P. Tovstik4.1 Introduction 4.2 Mathieu Equation 4.3 Model of the Flexible Rod of the Kapitsa Pendulum4.4 Asymptotic Expansion4.5 Pade Approximation 4.6 Discussion of Results 4.6.1 Resonances of Longitudinal Vibrations 4.6.2 General Picture of Stability by Asymptotic Formulas 4.6.3 Comparison with the Exact Solution 4.6.4 Conclusions4.7 Some Hypotheses Regarding the Possible Application of the Kapitsa Pendulum Effect in Modern and Advanced Technology References 5 Dynamic Properties of Periodic Structures with Symmetric InclusionsLudmila Ya. Banakh and Igor S. Pavlov5.1 Introduction 5.2 Oscillations of Symmetric ????-gon Frames 5.3 Oscillations of Periodic Systems Containing Symmetric Subsystems5.4 An Example of Calculation of a 3-Section System with Symmetric Subsystems 5.5 Structure of the Spectrum of Natural Frequencies of a Multisection Structure 5.6 Conclusions Appendix A. Application of the Group Representation Theory for Mechanical Systems A.1. Basic Concepts of the Representation Theory of Symmetry Groups A.2. Matrix Symmetry Operators References 6 Mathematical Model for Myopia Correction with MyoRing Implants Svetlana M. Bauer, Liudmila A. Venatovskaya, Eva B. Voronkova, Vladimir V. Kornikov, Larisa A. Avershina, and Anna E. Terenteva6.1 Introduction 6.2 Problem Statement 6.3 Results and Discussion 6.4 Conclusion References 7 Numerical Modeling the Stresses in Incompressible and Rigid Bodies Nikolai M. Bessonov and Yaroslava I. Litvinova7.1 Introduction 7.2 Numerical Modeling of the Flow of the Incompressible Micropolar Liquids 7.3 Numerical Modeling of the Deformation of a Rubber-Like Incompressible Solid Body 7.4 Numerical Modeling of Stresses in the Rigid Body 7.4.1 First Example 7.4.2 Second Example Appendix A: 3D Iterative Alternative Direction Implicit Method References 8 Three-Dimensional Numerical Analysis of Natural Vibrations and Stability of Cylindrical Shells Interacting with Fluid Sergey A. Bochkarev, Sergey V. Lekomtsev, Valerii P. Matveenko, and Alexander N. Senin8.1 Introduction 8.2 Mathematical and Numerical Formulations 8.3 Single Cylindrical Shells 8.3.1 Circular Cylindrical Shells 8.3.2 Elliptical Cylindrical Shells 8.4 System of two Circular Cylindrical Shells 8.4.1 Coaxial Shells 8.4.2 Eccentric shells 8.5 Conclusion References 9 On the Problem of Modeling the Influence of Ice Cover and Surface Waves of a Liquid on the Dynamics of a Floating Body Anastasiia A. Chevrychkina, Nikolai M. Bessonov, and Andrei K. Abramian9.1 Introduction 9.2 Statement of the Problem 9.3 Numerical Method 9.4 Results 9.5 Conclusion References 10 Nonlinear Stationary Waves in a Thin-Walled Bar Affected by Deplanation of Its Cross-Section in Torsion Vladimir Erofeev, Boris Lampsi (Jr.), Anna Leonteva, and Nadezhda Semerikova10.1 Introduction 10.2 Differential Equation for Torsional Vibrations of a Bar Taking into Account the Nonlinearity and Deplanation of the Bar Cross Section10.3 Wave Processes in a Thin-Walled Bar Taking into Account the Quadratic Nonlinearity 10.4 Wave Processes in a Thin-Walled Bar Taking into Account the Cubic Nonlinearity 10.5 Wave Processes in a Thin-Walled Bar with Simultaneous Consideration to the Quadratic and Cubic Nonlinearities 10.6 Conclusions References 11 Linear Reduced Elastic Isotropic Cosserat Medium Subjected to the External Follower Viscoelastic Torque as a Smart Acoustic Metamaterial Elena F. Grekova and Sabina M. Isaeva11.1 Introduction and Notation 11.2 Equations of the Reduced Elastic Linear Isotropic Cosserat Medium Subjected to a Viscoelastic Follower Body Torque Spectral Problem 11.3 Isotropic Linear Elastic Reduced Cosserat Medium Subjected to an Elastic Follower Torque 11.4 Isotropic Elastic Reduced Cosserat Medium Subjected to a Viscous or Viscoelastic Follower Torque 11.4.1 Dispersion Relation for the Shear–Rotational Wave 11.4.2 Small Dissipation far from Characteristic Frequencies O = O1 and O = 1 11.4.2.1 Real Part of the Wave Number 11.4.2.2 Imaginary Part of the Wave Number 11.4.2.3 Logarithmic Decrement 11.4.3 Small Dissipation near the Lower Characteristic Frequency O1 11.4.4 Small Dissipation near the Upper Characteristic Frequency O = 1 11.5 Conclusions References 12 Nonlinear Vibrations of Bimodular Continua by Means of Isogeometric Analysis 

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9783031437359
• Collana: Advanced Structured Materials
• Dimensioni: 235 x 155 mm Ø 1008 gr
• Formato: Copertina rigida
• Illustration Notes: XXIV, 480 p. 219 illus., 136 illus. in color.
• Pagine Arabe: 480
• Pagine Romane: xxiv