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Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

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Abstract

The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth-order Runge–Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender pipes.

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  • 22 November 2018

    In all the articles in Acta Mechanica Solida Sinica, Volume 31, Issues 1–4, the copyright is incorrectly displayed as “The Chinese Society of Theoretical and Applied Mechanics and Technology ” where it should be “The Chinese Society of Theoretical and Applied Mechanics”.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11622216 and 51409134).

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Authors and Affiliations

  1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhi-Yuan Liu & Lin Wang

  2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan, 430074, China

    Zhi-Yuan Liu & Lin Wang

  3. Tianjin Research Institute Water Transport Engineering, M.O.T., Test Detection Center of Water Transport Engineering, Tianjin, 300456, China

    Xi-Ping Sun

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  1. Zhi-Yuan Liu
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Correspondence to Lin Wang.

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Liu, ZY., Wang, L. & Sun, XP. Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid. Acta Mech. Solida Sin. 31, 32–50 (2018). https://doi.org/10.1007/s10338-018-0011-0

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  • DOI: https://doi.org/10.1007/s10338-018-0011-0

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