This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France.
The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.
Author(s): Igor V. Andrianov
Series: Advanced Structured Materials
Publisher: Springer
Year: 2018
Language: English
Pages: 0
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
