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A fatigue life analysis method for shallow curved hydraulic pipes with unstable alternating stress

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Abstract

Fatigue failure of hydraulic pipes, resulting from unstable alternating stress, is a common type of failure for hydraulic systems. In engineering, the reality of working with perfect straight pipes is nonexistent. Instead, the fatigue life of shallow curved pipes is an essential topic worth careful consideration and discussion. The purpose of this paper is to investigate the effect of dual-frequency excitation on the fatigue life of hydraulic pipes with an initial curved shape exposed to unstable alternating stress. Firstly, the governing equation of the shallow curved pipe is established by the generalized Hamilton principle. Secondly, the nonlinear partial differential integral equation is discretized into a set of nonlinearly coupled ordinary differential equations (ODEs) through Galerkin method. The effectiveness of GM (Galerkin method) is verified using DQEM (Differential quadrature element method). Upon this, the influence of the frequency difference between two frequencies on the forced vibration of the pipe midpoint is discussed. The phenomena of bifurcation and chaos in the transverse vibration of a system near the first natural frequency are analyzed exhaustively. The analysis shows that a low gap of frequency causes chaotic behavior. The Fourier series expansion technique is used to decouple the unstable alternating stress generated when chaos occurs. Based on Pairs theory, the linear combination mechanism of pipe life under decoupling stress is proposed, and the fatigue life of pipe under chaos is predicted. Finally, the potential impact of chaos on pipe fatigue life is investigated. The results of this research project expand the theoretical research field of pipe dynamics, provide effective research methods for a precise understanding of the entire lifecycle of pipe structures, and thus yield valuable insights and guidance for the reliability design, system management, maintenance of pipes, and fault prediction of pipe systems.

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Funding

The authors gratefully acknowledge the support of the National Science Fund for Distinguished Young Scholars (No.12025204).

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Authors and Affiliations

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

    Zhong-Jie Zhang & Jun-Ning Zhang

  2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Frontier Science Center of Mechanoinformatics, Shanghai Institute of Applied Mathematics and Mechanics, Shool of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

    Jun-Ning Zhang, Hu Ding & Li-Qun Chen

  3. College of Mechanical and Electrical Engineering, Nan**g University of Aeronautics and Astronautics, Nan**g, 210016, China

    Zhong-Jie Zhang

  4. Shaoxing Institute of Technology, Shanghai University, Shaoxing, 312074, China

    Hu Ding

  5. Shanghai Institute of Applied Mathematics and Mechanics, 149 Yan Chang Road, Shanghai, 200072, China

    Jun-Ning Zhang

Authors
  1. Zhong-Jie Zhang
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Contributions

Investigation, writing—review & editing contributed by Zhong-Jie Zhang; conceptualization, writing—original draft & writing—review contributed by Jun-Ning Zhang; funing, writing—review & editing contributed by Hu Ding; writing—review & editing contributed by Li-Qun Chen; All authors have read and agreed to the published version of the manuscript.

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Correspondence to Jun-Ning Zhang.

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Zhang, ZJ., Zhang, JN., Ding, H. et al. A fatigue life analysis method for shallow curved hydraulic pipes with unstable alternating stress. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01452-1

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  • DOI: https://doi.org/10.1007/s40435-024-01452-1

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