Bifurcation and chaos of a flag in an inviscid flow

被引:38
作者
Chen, Ming [1 ]
Jia, Lai-Bing [1 ]
Wu, Yan-Feng [1 ]
Yin, Xie-Zhen [1 ]
Ma, Yan-Bao [2 ]
机构
[1] Univ Sci & Technol China, Dept Modern Mech, Hefei 230027, Anhui, Peoples R China
[2] Univ Calif, Merced, CA 95343 USA
关键词
Fluid-structure interactions; Flutter instability; Bifurcation; Chaos; CANTILEVERED FLEXIBLE PLATES; IMMERSED BOUNDARY METHOD; AXIAL-FLOW; PAPER FLUTTER; POINT-VORTEX; UNIFORM-FLOW; SOAP FILM; INSTABILITY; FILAMENTS; DYNAMICS;
D O I
10.1016/j.jfluidstructs.2013.11.020
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
A two-dimensional model is developed to study the flutter instability of a flag immersed in an inviscid flow. Two dimensionless parameters governing the system are the structure-to-fluid mass ratio M* and the dimensionless incoming flow velocity U*. A transition from a static steady state to a chaotic state is investigated at a fixed M*=1 with increasing U*. Five single-frequency periodic flapping states are identified along the route, including four symmetrical oscillation states and one asymmetrical oscillation state. For the symmetrical states, the oscillation frequency increases with the increase of U*, and the drag force on the flag changes linearly with the Strouhal number. Chaotic states are observed when U* is relatively large. Three chaotic windows are observed along the route. In addition, the system transitions from one periodic state to another through either period-doubling bifurcations or quasi-periodic bifurcations, and it transitions from a periodic state to a chaotic state through quasi-periodic bifurcations. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码:124 / 137
页数:14
相关论文
共 36 条
[1]   Nonlinear dynamics of silk and Mylar flags flapping in axial flow [J].
Abderrahmane, Hamid Ait ;
Paidoussis, Michael P. ;
Fayed, Mohamed ;
Ng, Hoi Dick .
JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS, 2012, 107 :225-236
[2]  
Ait Abderrahmane H., 2011, PHYS REV E, V84
[3]   Drag reduction through self-similar bending of a flexible body [J].
Alben, S ;
Shelley, M ;
Zhang, J .
NATURE, 2002, 420 (6915) :479-481
[4]   Optimal flexibility of a flapping appendage in an inviscid fluid [J].
Alben, Silas .
JOURNAL OF FLUID MECHANICS, 2008, 614 :355-380
[5]   Flapping states of a flag in an inviscid fluid: Bistability and the transition to chaos [J].
Alben, Silas ;
Shelley, Michael J. .
Fluid Dynamics Research, 2014, 46 (05)
[6]   The attraction between a flexible filament and a point vortex [J].
Alben, Silas .
JOURNAL OF FLUID MECHANICS, 2012, 697 :481-503
[7]  
Auregan Y, 1995, J SOUND VIB, V188, P39, DOI 10.1006/jsvi.1995.0577
[8]  
Connell B.S, 2006, THESIS MIT CAMBRIDGE
[9]   Flapping dynamics of a flag in a uniform stream [J].
Connell, Benjamin S. H. ;
Yue, Dick K. P. .
JOURNAL OF FLUID MECHANICS, 2007, 581 :33-68
[10]   INSTABILITY OF AN ELASTIC STRIP HANGING IN AN AIRSTREAM [J].
DATTA, SK ;
GOTTENBERG, WG .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1975, 42 (01) :195-198