Control of localized non-linear strain waves in complex crystalline lattices

被引：7

作者：

Porubov, A. V. ^{[1
,2
,3
]}

Antonov, I. D. ^{[3
]}

Fradkov, A. L. ^{[1
,2
]}

Andrievsky, B. R. ^{[1
,4
]}

机构：

[1] Inst Problems Mech Engn, VO, Bolshoy 61, St Petersburg 199178, Russia

[2] St Petersburg State Univ, VO, 7-9 Univ Skaya Nab, St Petersburg 199034, Russia

[3] St Petersburg State Polytech Univ, Polytech Skaya St 29, St Petersburg 195251, Russia

[4] ITMO Univ, Kronverkskiy Pr 49, St Petersburg 197101, Russia

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2016年 / 86卷

基金：

俄罗斯科学基金会;

关键词：

Crystalline lattice; Non-linear strain wave; Feedback control; Numerical solution; FEEDBACK-CONTROL; DYNAMICS; SYSTEMS;

D O I：

10.1016/j.ijnonlinmec.2016.09.002

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The distributed feedback control is developed to support propagation of localized non-linear waves for the double sine-Gordon equation and the dispersive sine-Gordon equation previously obtained for the description of dynamic processes in complex crystalline lattices. The control allows the propagation of both bell-shaped and kink-shaped waves with permanent shape and velocity, with a functional form which does not correspond to the known analytical solutions of the equations. The results might be used for choosing external loading providing desired strain localization or variations in the internal structure of the lattice. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：174 / 184

页数：11

共 32 条

[1] Dynamics and control of oscillations in a complex crystalline lattice [J].

Aero, E ;

Fradkov, A ;

Andrievsky, B ;

Vakulenko, S .

PHYSICS LETTERS A, 2006, 353 (01) :24-29

[2] Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids [J].

Aero, E. L. ;

Bulygin, A. N. .

MECHANICS OF SOLIDS, 2007, 42 (05) :807-822

[3] Micromechanics of a double continuum in a model of a medium with variable periodic structure [J].

Aero, E. L. .

JOURNAL OF ENGINEERING MATHEMATICS, 2006, 55 (1-4) :81-95

[4]

Askar A., 1985, Lattice Dynamical Foundations of Continuum Theories

[5]

Bogdan M., 1997, Proceedings of the Estonian Academy of Sciences. Physics, Mathematics, V46, P14

[6]

Bogdan M. M., 1999, Condensed Matter Physics, V2, P255

[7]

Born M., 1954, Dynamic Theory of Crystal Lattice

[8]

Braun O.M., 2004, TEXT MONOGR

[9]

Butkovsky A.G., 1969, Distributed Control System

[10] OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS (A SURVEY OF SOVIET PUBLICATIONS) [J].

BUTKOVSKY, AG ;

EGOROV, AI ;

LURIE, KA .

SIAM JOURNAL ON CONTROL, 1968, 6 (03) :437-+

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