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Nonlinear vibration of slightly curved pipe with conveying pulsating fluid

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Abstract

The nonlinear governing motion equation of slightly curved pipe with conveying pulsating fluid is set up by Hamilton’s principle. The motion equation is discretized into a set of low dimensional system of nonlinear ordinary differential equations by the Galerkin method. Linear analysis of system is performed upon this set of equations. The effect of amplitude of initial deflection and flow velocity on linear dynamic of system is analyzed. Curves of the resonance responses about \(\varOmega \approx {\omega _\mathrm{{1}}}\) and \(\varOmega \approx \mathrm{{2}}{\omega _\mathrm{{1}}}\) are performed by means of the pseudo-arclength continuation technique. The global nonlinear dynamic of system is analyzed by establishing the bifurcation diagrams. The dynamical behaviors are identified by the phase diagram and Poincare maps. The periodic motion, chaotic motion and quasi-periodic motion are found in this system.

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Acknowledgements

This work was partly Supported by the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (2016QZJ03), Sichuan University of Science & Engineering fund (2015KY02), Fund Project of Sichuan University of Science & Engineering in hit-haunting for talents (No. 2016RCL31) and Found of Science & Technology Department of Sichuan Province (Grant No. 2016JQ0046).

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  1. School of Science, Sichuan University of Science & Engineering, Zigong, 643000, China

    Yun-dong Li

  2. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Yi-ren Yang

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  1. Yun-dong Li
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Correspondence to Yun-dong Li.

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Li, Yd., Yang, Yr. Nonlinear vibration of slightly curved pipe with conveying pulsating fluid. Nonlinear Dyn 88, 2513–2529 (2017). https://doi.org/10.1007/s11071-017-3393-5

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  • DOI: https://doi.org/10.1007/s11071-017-3393-5

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