1 A Semi-Empirical Fluid Force Model for Vortex-Induced Vibration of an Elastic Structure
Andrei K. Abramian and Sergey A. Vakulenko
1.1 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 Furtmüller
2.1 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. Eremeyev
3.1 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. Tovstik
4.1 Introduction
4.2 Mathieu Equation
4.3 Model of the Flexible Rod of the Kapitsa Pendulum
4.4 Asymptotic Expansion
4.5 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 Conclusions
4.7 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 Inclusions
Ludmila Ya. Banakh and Igor S. Pavlov
5.1 Introduction
5.2 Oscillations of Symmetric ????-gon Frames
5.3 Oscillations of Periodic Systems Containing Symmetric Subsystems
5.4 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. Terenteva
6.1 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. Litvinova
7.1 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. Senin
8.1 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. Abramian
9.1 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 Semerikova
10.1 Introduction
10.2 Differential Equation for Torsional Vibrations of a Bar Taking into Account the Nonlinearity and Deplanation of the Bar Cross Section
10.3 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. Isaeva
11.1 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
