Problems of Nonlinear Mechanics and Physics of Materials

Part I Stationary and Non-stationary Dynamics of Oscillators and
Oscillatory Chains
Wide Frequency Higher-Order Dynamic Model for Transient
Waves in a Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Igor V. Andrianov, Vladyslav V. Danishevskyy, Julius D. Kaplunov
and Bernd Markert
Analysis of the Beating States in the System of Nonlinearly
Coupled Parametrically Forced Oscillators . . . . . . . . . . . . . . . . . . . . . . 13
V. Kislovsky and Y. Starosvetsky
Is Energy Localization Possible in the Conditions of Non-local
Acoustic Vacuum? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Irina P. Koroleva (Kikot) and Leonid I. Manevitch
Phase Dynamics of Intrinsic Localized Modes in Two Weakly
Coupled Nonlinear Chains and Correspondence Between Periodic
Tunneling of Classical and Quantum Objects . . . . . . . . . . . . . . . . . . . . 39
Yuriy A. Kosevich
Non-linear Beatings as Non-stationary Synchronization of Weakly
Coupled Autogenerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Margarita A. Kovaleva, Leonid I. Manevitch and Valery N. Pilipchuk
Normal Modes of Chaotic Vibrations and Transient Normal
Modes in Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Yuri V. Mikhlin, Katarina Yu. Plaksiy, Tatyana V. Shmatko
and Gayane V. Rudneva
Advanced Nonlinear System Identification for Modal Interactions in
Nonlinear Structures: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
K. J. Moore, A. Mojahed, M. Kurt, M. Eriten, D. M. McFarland,
L. A. Bergman and A. F. Vakakis
ix
Non-smooth Spatial and Temporal Substitutions in
Impact Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Valery N. Pilipchuk
Revolution of Pendula: Rotational Dynamics of the Coupled
Pendula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Valeri V. Smirnov
Plane Motion of a Rigid Body Suspended on Nonlinear
Spring-Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Roman Starosta, Grażyna Sypniewska-Kamińska and Jan Awrejcewicz
Part II Molecular Dynamics of Polymer Crystals and
Nanostructures
Supermolecular Structure Formation During Electrospinning, and Its
Effect on Electrospun Polymer Nanofiber Unique Features . . . . . . . . . . 173
Arkadii Arinstein
Recent Developments in Theory and Modeling of Polymer-Based
Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Valeriy V. Ginzburg
B$A Transition in a Short DNA Molecule . . . . . . . . . . . . . . . . . . . . . . 225
Natalya A. Kovaleva and Elena A. Zubova
2D Chain Models of Nanoribbon Scrolls . . . . . . . . . . . . . . . . . . . . . . . . 241
Alexander V. Savin and Mikhail A. Mazo
Interaction Between DNA Molecule and Nanosize Pore . . . . . . . . . . . . . 263
Robert A. Turusov
Part III Condensed Matter Mechanics and Physics
Wave-Particle Duality and Quantum-Classical Analogy . . . . . . . . . . . . . 273
Leonid I. Manevitch
Molecular Simulation of Plastic Deformation of Oligomer Systems . . . . 303
Mikhail A. Mazo, Ivan A. Strelnikov, N. K. Balabaev
and Alexander A. Berlin
Plastic Deformation in Disordered Solids: The State of the Art
and Unresolved Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Eduard F. Oleinik, Mikhail A. Mazo, Michael I. Kotelyanskii,
Sergey N. Rudnev and Olga B. Salamatina
Shockwaves and Kinks in Exothermic Nonlinear Chains . . . . . . . . . . . . 333
Itzik B. Shiroky and Oleg V. Gendelman
x Contents
Part IV Theory of Beams, Plates and Shells
Local Buckling of Cylindrical Shells. Pogorelov’s Geometrical
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
A. Yu. Evkin
Stretching of Reinforced Orthotropic Plate . . . . . . . . . . . . . . . . . . . . . . 393
S. Koblik
Features of Deformation of Smooth and Stringer Cylindrical Shells at
Axial Compression and Statistical Properties of Their
Critical Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Vasiliy L. Krasovsky
Discontinuities in Viscoelastic Timoshenko Beam Under
Moving Concentrated Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
Arkadiy I. Manevich
Part V Theory of Elasticity and Thermo-elasticity
Analytical Study of a Nonlinear Beam Including a Piezoelectric
Patch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
V. Guillot, A. Ture Savadkoohi and C.-H. Lamarque
On Higher Order Effective Boundary Conditions for a Coated
Elastic Half-Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
Julius Kaplunov, Danila Prikazchikov and Leyla Sultanova
Electrically Plane and Mechanically Antiplane Problem for an
Inclusion with Stepwise Rigidity Between Piezoelectric Materials . . . . . 463
Vladimir V. Loboda, Anna G. Kryvoruchko and Alla Ye. Sheveleva
Thermomechanical Coupling and Transient to Steady Global
Dynamics of Orthotropic Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
Valeria Settimi and Giuseppe Rega
Appendix: Professional Life of Professor Leonid Isakovich
Manevitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .