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Math. Comput. Appl. 2010, 15(3), 490-502; doi:10.3390/mca15030490

Bifurcation and Chaos of Slightly Curved Pipes

Celal Bayar University, Civil Engineering Department, Manisa, Turkey
Published: 1 December 2010
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Abstract

Non-linear vibrations of slightly curved pipes conveying fluid with constant velocity are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is considered due to the geometry of the pipe itself. The ends of the curved pipe are assumed to be immovable simple supports. The equations of motion of pipes are derived using Hamilton's principle and solved by Galerkin method. The bifurcation diagrams are presented for various amplitudes of the curvature function and fluid velocity. The periodic and chaotic motions have been observed in the transverse vibrations of slightly curved pipe conveying fluid.
Keywords: Slightly curved pipe; conveying fluid; nonlinear vibration; Galerkin method; bifurcation Slightly curved pipe; conveying fluid; nonlinear vibration; Galerkin method; bifurcation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Sinir, B.G. Bifurcation and Chaos of Slightly Curved Pipes. Math. Comput. Appl. 2010, 15, 490-502.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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