Bifurcations and chaotic motions of a curved pipe conveying fluid with nonlinear constraints

This paper investigates the bifurcations and chaotic motions of a fluid-conveying curved pipe restrained with nonlinear constraints. The nonlinear equation of motion for the curved pipe is derived by forces equilibrium on microelement of the system under consideration. Depending on the nonlinear equation of motion and the corresponding boundary conditions for the curved pipe, the DQM (differential quadrature method) is introduced to formulate the discrete forms of the equation of motion for the system, which is then solved by numerical methods. Calculations of phase-plane portraits, time history diagrams, PS (Power Spectrum) diagrams, bifurcation diagrams and Poincare maps of the oscillations establish clearly the existence of the chaotic motions. In addition, the result shows the route to chaos for the pipe is via period-doubling bifurcations, which is affected definitively by several parameters of the system.

[1]  J.-D. Jin.  STABILITY AND CHAOTIC MOTIONS OF A RESTRAINED PIPE CONVEYING FLUID , 1997 .

[2]  Shoei‐sheng Chen,et al.  Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid , 1973 .

[3]  C. Dupuis,et al.  The equations of motion of curved pipes conveying fluid , 1992 .

[4]  Yuying,et al.  DIFFERENTIAL QUADRATURE METHOD TO STABILITY ANALYSIS OF PIPES CONVEYING FLUID WITH SPRING SUPPORT , 2000 .

[5]  Earl H. Dowell,et al.  Chaotic oscillations of a cantilevered pipe conveying fluid , 1988 .

[6]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[7]  S. S. Chen.  FLOW-INDUCED IN-PLANE INSTABILITIES OF CURVED PIPES. , 1972 .

[8]  M. P. Païdoussis,et al.  Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid , 1989 .

[9]  C. Dupuis,et al.  Application of the transfer matrix method to non-conservative systems involving fluid flow in curved pipes , 1985 .

[10]  Charles W. Bert,et al.  A perturbation solution for non-linear vibration of uniformly curved pipes conveying fluid , 1986 .

[11]  M. P. Païdoussis,et al.  On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory , 1988 .

[12]  Shoei‐sheng Chen,et al.  Vibration and Stability of a Uniformly Curved Tube Conveying Fluid , 1972 .

[13]  M. P. Païdoussis,et al.  Stability, double degeneracy and chaos in cantilevered pipes conveying fluid , 1994 .

[14]  G. Steven Gipson,et al.  Instability of Internally Damped Curved Pipes , 1990 .