Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

Yi Xiang Geng; Han Ze Liu

doi:10.4028/www.scientific.net/AMM.444-445.791

Paper Titles

Property of Conjugacy between Two Chaos Maps
p.771

Evolution Model Analysis for Comprehensive Transportation Structure
p.775

A New Approach for the Shape Optimization of Complex Nonlinear Structures
p.780

A Simple Numerical Simulation Method for Lorenz System Families
p.786

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation
p.791

Stability of Subharmonic Oscillations in a Pipe Conveying Fluid under Harmonic Excitation
p.796

Model Analysis for Comprehensive Transportation Structure Evolution Based on Catastrophe Theory
p.801

Levitation System Controller Design Based on the Implicit General Predictive Control Algorithm
p.806

Strength and Displacement Analysis of a Nuclear Power Giant Lifting Grid and Steel Liner
p.815

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 444-445Subharmonic Bifurcations and Transition to Chaos...

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

Abstract:

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

You might also be interested in these eBooks

Advances in Computational Modeling and Simulation

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 444-445)

Pages:

791-795

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.444-445.791

Citation:

Cite this paper

Online since:

October 2013

Authors:

Yi Xiang Geng, Han Ze Liu

Keywords:

Chaotic Dynamics, Homoclinic Bifurcations, Melnikov Method, Pipe Conveying Fluid, Subharmonic Bifurcations

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] M.P. Paidoussis, G.X. Li, Pipes conveying fluid: a model dynamical problem, J. Fluids Struct. 7(1993)137-204.

Google Scholar

[2] M.P. Paidoussis, G.X. Li, F.C. Moon, Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid, J. Sound Vib. 135(1)(1989)1-19.

DOI: 10.1016/0022-460x(89)90750-5

Google Scholar

[3] M.P. Paidoussis, N.T. Issid, Dynamic stability of pipes conveying fluid, J. Sound Vib. 33(1974)267-294.

DOI: 10.1016/s0022-460x(74)80002-7

Google Scholar

[4] M.P. Paidoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow, Academic Press, London, (1998).

Google Scholar

[5] J.D. Jin, Satbility and chaotic motions of a restrained pipe conveying fluid, J. Sound Vib. 208(3)(1997)427-439.

DOI: 10.1006/jsvi.1997.1195

Google Scholar

[6] C. Semler, G.X. Li, M.P. Paidoussis, The non-linear equations of motion of pipes conveying fluid, J. Sound Vib. 169(1994)577-599.

DOI: 10.1006/jsvi.1994.1035

Google Scholar

[7] G.S. Zou, J.D. Jin, Y. Han, Stability and chaotic vibrations of a pipe conveying fluid under harmonic excitation, J. Shanghai Univ. 4(3)(2000)179-185.

DOI: 10.1007/s11741-000-0058-1

Google Scholar

[8] R.D. Bao, W.J. Bi, B.C. Wen, Predicting chaotic motion of a two end-fixed fluid conveying pipe, J. vibr. shock, 27(6)(2008)99-102.

Google Scholar

[9] J.M.T. Thompson, P. Holmes, Nonlinear Dynamics and Chaos, Wiley, New York, (1987).

Google Scholar

[10] J.B. Li, H.H. Dai, On the study of singular nonlinear traveling wave equations: Dynamical system approach, Science Press, Beijing, (2007).

Google Scholar