Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-Dimensional Models

被引:26
作者
Kuznetsov, Sergey P. [1 ]
机构
[1] RAS, Kotelnikovs Inst Radio Engn & Elect, Saratov Branch, Saratov 410019, Russia
关键词
body motion in a fluid; oscillations; autorotation; flutter; attractor; bifurcation; chaos; Lyapunov exponent; NONHOLONOMIC MODEL; BEHAVIOR; MOTION; FLUTTER; TUMBLE; PAPER; BODY;
D O I
10.1134/S1560354715030090
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Results are reviewed concerning the planar problem of a plate falling in a resisting medium studied with models based on ordinary differential equations for a small number of dynamical variables. A unified model is introduced to conduct a comparative analysis of the dynamical behaviors of models of Kozlov, Tanabe-Kaneko, Belmonte-Eisenberg-Moses and Andersen-Pesavento-Wang using common dimensionless variables and parameters. It is shown that the overall structure of the parameter spaces for the different models manifests certain similarities caused by the same inherent symmetry and by the universal nature of the phenomena involved in nonlinear dynamics (fixed points, limit cycles, attractors, and bifurcations).
引用
收藏
页码:345 / 382
页数:38
相关论文
共 63 条
[1]   Unsteady aerodynamics of fluttering and tumbling plates [J].
Andersen, A ;
Pesavento, U ;
Wang, ZJ .
JOURNAL OF FLUID MECHANICS, 2005, 541 (541) :65-90
[2]   Analysis of transitions between fluttering, tumbling and steady descent of falling cards [J].
Andersen, A ;
Pesavento, U ;
Wang, ZJ .
JOURNAL OF FLUID MECHANICS, 2005, 541 :91-104
[3]  
[Anonymous], J REINE ANGEW MATH
[4]  
[Anonymous], 1978, ZH EKSP TEOR FIZ, V74, P1366
[5]  
[Anonymous], 2004, Elements of Applied Bifurcation Theory
[6]  
[Anonymous], 2005, DYNAMICS RIGID BODY
[7]  
[Anonymous], 1990, VESTN MOSK U 1, P79
[8]  
[Anonymous], 2011, Theory of Oscillators
[9]  
Arzhanikov NS, 1983, AERODYNAMICS AIRCRAF
[10]  
Belmonte A, 1999, PHYS WORLD, V12, P21