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Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity

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Abstract

Considering that the fluid-conveying pipes made of fractional-order viscoelastic material such as polymeric materials with pulsatile flow are widely applied in engineering, we focus on the stability and bifurcation behaviors in parametric resonance of a viscoelastic pipe resting on an elastic foundation. The Riemann–Liouville fractional-order constitutive equation is used to accurately describe the viscoelastic property. Based on this, the nonlinear governing equations are established according to the Euler–Bernoulli beam theory and von Karman’s nonlinearity, with using the generalized Hamilton’s principle. The stability boundaries and steady-state responses undergoing parametric excitations are determined with the aid of the direct multiple-scale method. Some numerical examples are carried out to show the effects of fractional order and viscoelastic coefficient on the stability region and nonlinear bifurcation behaviors. It is noticeable that the fractional-order viscoelastic property can effectively reconstruct the dynamic behaviors, indicating that the stability of the pipes can be conspicuously enhanced by designing and tuning the fractional order of viscoelastic materials.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11902001, 12132010), Postgraduate Scientific Research Project of Institutions of Higher Education in Anhui Province (YJS20210445), Anhui Provincial Natural Science Foundation (No.1908085QA13) and the Middle-aged Top-notch Talent Program of Anhui Polytechnic University.

Funding

National Natural Science Foundation of China, 11902001, Ye Tang, 12132010, Qian Ding.

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Authors and Affiliations

  1. School of Mechanical Engineering, Anhui Polytechnic University, Wuhu, 241000, China

    Ye Tang & Guo Wang

  2. Department of Mechanics, Tian** University, Tian**, 300350, China

    Ye Tang & Qian Ding

Authors
  1. Ye Tang
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  2. Guo Wang
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  3. Qian Ding
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Correspondence to Qian Ding.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Tang, Y., Wang, G. & Ding, Q. Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity. Acta Mech. Solida Sin. 35, 733–745 (2022). https://doi.org/10.1007/s10338-022-00328-1

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  • DOI: https://doi.org/10.1007/s10338-022-00328-1

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