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Natural Frequencies, Critical Velocity and Equilibriums of Fixed–Fixed Timoshenko Pipes Conveying Fluid

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Abstract

In this paper, the free vibration characteristics of fixed–fixed Timoshenko pipe conveying fluid, including natural frequency, mode, critical velocity, bifurcation of static equilibrium configuration, are studied analytically and numerically. Based on the Timoshenko beam theory and generalized Hamilton principle, a vibration model of pipes conveying fluid with fixed–fixed boundary conditions is established. The analytical expressions of critical flow velocity and supercritical nontrivial static equilibrium configuration are derived. The natural frequencies are studied by the complex modal method (CMM) and the Galerkin truncation method (GTM). Moreover, the finite element method (FEM) is developed to deal with the influence of fluid velocity on the vibration characteristics of the pipe. The gyroscopic force caused by the fluid flow is equivalent to the dam** matrix. It shows that the natural frequencies of the FEM agree well with the theoretical results of CMM and GTM in general. However, the developed FEM cannot reflect the influence of the fluid flow on the vibration mode of pipes. Furthermore, the free vibration characteristics of the pipe are significantly affected by the internal pressure of the pipe.

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Data Availability

The data that support the findings of this study are available from the corresponding author [H. Ding], upon reasonable request.

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Acknowledgements

The authors gratefully acknowledge the support of the National Science Fund for Distinguished Young Scholars (No. 12025204) and the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018).

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The authors declare they have no financial interests.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

    Yu-Fei Shao & Li-Qun Chen

  2. University of Science and Technology of China, Anhui, 230026, China

    **n Fan

  3. State-Owned Machinery Factory in Wuhu, Wuhu, 241007, China

    Song Shu

  4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, 99 Shangda road, Shanghai, 200444, China

    Hu Ding

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Correspondence to Hu Ding.

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Shao, YF., Fan, X., Shu, S. et al. Natural Frequencies, Critical Velocity and Equilibriums of Fixed–Fixed Timoshenko Pipes Conveying Fluid. J. Vib. Eng. Technol. 10, 1623–1635 (2022). https://doi.org/10.1007/s42417-022-00469-0

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