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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(3), 490-502;

Bifurcation and Chaos of Slightly Curved Pipes

Celal Bayar University, Civil Engineering Department, Manisa, Turkey
Published: 1 December 2010
PDF [473 KB, uploaded 4 April 2016]


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

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