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Stability and Chaotic Vibrations of a Fluid-Conveying Pipe with Additional Combined Constraints

Published online by Cambridge University Press:  05 May 2011

L. Wang ,
Q. Ni  and
Y. Y. Huang
L. Wang*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P.R., China
Q. Ni*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P.R., China
Y. Y. Huang*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P.R., China
*
*Ph.D., correspondence author
**Professor
**Professor
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Abstract

The stability and possible chaotic vibrations of a fluid-conveying pipe with additional combined constraints are investigated. The pipe, restrained by motion constraints somewhere along the length of the pipe, is modeled by a beam clamped at the left end and supported by a special device (a rotational elastic constraint plus a Q-apparatus) at the right end. The motion constraints are modeled by both cubic and trilinear models. Based on the Differential Quadrature Method (DQM), the nonlinear dynamical equations of motion for the system are formulated, and then solved via a numerical iterative technique. Calculations of bifurcation diagrams, phase portraits, time responses and Poincare maps of the oscillations establish the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations. It is found that the effect of spring constant of the rotational elastic constraint on the dynamics is significant. Moreover, the critical fluid velocity at the Hopf bifurcation point for the cubic model is higher than that for the trilinear model.

Keywords

Fluid-conveying pipeChaotic vibrationStabilityCombined constraints.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 1 , March 2009 , pp. 85 - 93
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

1.Holmes, PJ., “Bifurcations to Divergence and Flutter in Flow-Induced Oscillations: A Finite-Dimensional Analysis,” Journal of Sound and Vibration, 53, pp. 471–503 (1977).CrossRefGoogle Scholar
2.Chen, SS., “Flow-Induced In-Plane Instabilities of Curved Pipes,” Nuclear Engineering and Design, 23, pp. 29–38 (1972).CrossRefGoogle Scholar
3.Paidoussis, MP. and Issid, NT., “Dynamic Stability of Pipes Conveying Fluid,” Journal of Sound and Vibration, 33, pp. 267–294 (1974).CrossRefGoogle Scholar
4.Misra, AK., Paidoussis, MP. and Van, KS., “On the Dynamics of Curved Pipes Transporting Fluid. Part I: Inextensible Theory,” Journal of Fluids and Structures, 2, pp. 211–244 (1988).Google Scholar
5.Misra, AK., Paidoussis, MP. and Van, KS., “On the Dynamics of Curved Pipes Transporting Fluid. Part II: Extensible Theory,” Journal of Fluids and Structures, 2, pp. 245–261 (1988).CrossRefGoogle Scholar
6.Tang, DM. and Do well, EH., “Chaotic Oscillations of a Cantilevered Pipe Conveying Fluid,” Journal of Fluids and Structures, 2, pp. 263–283 (1988).CrossRefGoogle Scholar
7.Païdoussis, MP. and Moon, FC., “Non-Linear and Chaotic Fluidelastic Vibrations of a Flexible Pipe Conveying Fluid,” Journal of Fluids and Structures, 3, pp. 567–591 (1988).CrossRefGoogle Scholar
8.Païdoussis, MP., Li, GX. and Moon, FC., “Chaotic Oscillations of the Autonomous System of a Constrained Pipe Conveying Fluid,” Journal of Sound and Vibration, 135, pp. 1–19 (1989).CrossRefGoogle Scholar
9.Païdoussis, MP., Li, GX. and Rand, RH., “Chaotic Motions of a Constrained Pipe Conveying Fluid: Comparison Between Simulation, Analysis and Experiment,” Journal of Applied Mechanics, 58, pp. 559–565 (1991).CrossRefGoogle Scholar
10.Païdoussis, MP., Cusumand, TP. and Copeland, GS., “Low-Dimensional Chaos in a Flexible Tube Conveying Fluid,” Journal of Applied Mechanics, 59, pp. 196–205 (1992).CrossRefGoogle Scholar
11.Païdoussis, MP. and Semler, C., “Nonlinear and Chaotic Oscillations of a Constrained Cantilevered Pipe Conveying Fluid: A Full Nonlinear Analysis,” Nonlinear Dynamics, 29, pp. 655–670 (1993).CrossRefGoogle Scholar
12.Ni, Q., Wang, L. and Qian, Q., “Chaotic Transients in a Curved Fluid Conveying Tube,” Acta Mechanica Solida Sinica, 18, pp. 207–214 (2005).Google Scholar
13.Qiao, N., Lin, W. and Qin, Q., “Bifurcations and Chaotic Motions of a Curved Pipe Conveying Fluid with Nonlinear Constraints,” Computers and Structures, 84, pp. 708–717 (2006).CrossRefGoogle Scholar
14.Dzhupanov, VA. and Lilkova-Markova, SV., “Dynamic Stability of a Fluid-Conveying Cantilevered Pipe on an Additional Combined Support,” International Applied Mechanics, 39, pp. 185–191 (2003).CrossRefGoogle Scholar
15.Dzhupanov, VA. and Lilkova-Markova, SV., “Divergent Instability Domains of a Fluid-Conveying Cantilevered Pipe with a Combined Support,” International Applied Mechanics, 40, pp. 319–321 (2004).CrossRefGoogle Scholar
16.Bert, CW. and Malik, M., “Differential Quadrature Method in Computational Mechanics: A Review,” Applied Mechanics Reviews, 49, pp. 1–27 (1996).CrossRefGoogle Scholar
17.Ni, Q. and Huang, YY., “Differential Quadrature Method to Stability Analysis of Pipes Conveying Fluid with Spring Support,” Acta Mechanica Solida Sinica, 13, pp. 320–327 (2000).Google Scholar