The nonlinear dynamics of elastic tubes conveying a fluid

被引：9
作者：
Beauregard, Matthew A. [1 ]
Goriely, Alain [1 ,2 ]
Tabor, Michael [1 ,2 ]
机构：
[1] Univ Arizona, Program Appl Math, Tucson, AZ 85721 USA
[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
来源：
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES | 2010年 / 47卷 / 01期
基金：
美国国家科学基金会;
关键词：
Elastic tubes; Pipe flow; Dean number; Kirchhoff equations; Dynamical instabilities; HELICAL PIPE-FLOW; UNSTABLE OSCILLATION; CURVED PIPES; SELF-CONTACT; RODS; DNA; STABILITY; FILAMENTS; TORSION; MECHANICS;
D O I：
10.1016/j.ijsolstr.2009.09.022
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：161 / 168
页数：8
相关论文
共 58 条
[1]  
[Anonymous], IMA
[2]  
[Anonymous], 1926, TREATISE MATH THEORY
[3]  
Antman SS, 1996, J NONLINEAR SCI, V6, P1
[4]   TRAVELING WAVES IN HYPERELASTIC RODS [J].
ANTMAN, SS ;
LIU, TP .
QUARTERLY OF APPLIED MATHEMATICS, 1979, 36 (04) :377-399
[5]  
ANTMAN SS, 1981, ARCH RATION MECH AN, V76, P289, DOI 10.1007/BF00249969
[6]  
Antman SS., 2005, Nonlinear Problems of Elasticity
[7]   ONSET OF WRITHING IN CIRCULAR ELASTIC POLYMERS [J].
BENHAM, CJ .
PHYSICAL REVIEW A, 1989, 39 (05) :2582-2586
[8]   ELASTIC MODEL OF THE LARGE-SCALE STRUCTURE OF DUPLEX DNA [J].
BENHAM, CJ .
BIOPOLYMERS, 1979, 18 (03) :609-623
[9]   GEOMETRY AND MECHANICS OF DNA SUPERHELICITY [J].
BENHAM, CJ .
BIOPOLYMERS, 1983, 22 (11) :2477-2495
[10]   FLOW IN CURVED PIPES [J].
BERGER, SA ;
TALBOT, L ;
YAO, LS .
ANNUAL REVIEW OF FLUID MECHANICS, 1983, 15 :461-512
123456