A mathematical model for non-linear dynamics of conservative systems with non-homogeneous boundary conditions

被引：1
|
作者：
Krysko, V. A. [1 ]
Awrejcewicz, J. [1 ]
Molodenkova, T. [1 ]
机构：
[1] Saratov Tech Univ, Dept Math, Saratov 410054, Russia
来源：
COMPUTERS & STRUCTURES | 2006年 / 84卷 / 29-30期
关键词：
bifurcation; chaos; plate; non-homogeneous boundary conditions; Feigenbaum scenario; Bubnov-Galerkin method;
D O I：
10.1016/j.compstruc.2006.08.018
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this work a transition into a chaotic dynamics of plates with unmovable boundary conditions along a plate contour and subjected to a longitudinal impact action modeled as a rectangular type loading of infinite length in time is studied. The well-known T. von Karman equations governing behaviour of flexible isotropic plates have been applied. Finite-difference approximation of order 0(h 4) allowed to transform the problem from PDEs to ODEs. We have shown and discussed how the investigated plate vibrations are transmitted into chaotic dynamics through a period doubling bifurcation. Furthermore, essential influence of boundary conditions on bifurcations number is illustrated, and for all investigated problems the Feigenbaum constant estimation is reported. (c) 2006 Elsevier Ltd. All rights reserved.
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页码：1918 / 1924
页数：7
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