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The Instability and Response Studies of a Top-Tensioned Riser under Parametric Excitations Using the Differential Quadrature Method

Author

Listed:
  • Yang Zhang

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Qiang Gui

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Yuzheng Yang

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Wei Li

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
    Hubei Key Laboratory of Naval Architecture & Ocean Engineering Hydrodynamics, Huazhong University of Science and Technology, Wuhan 430074, China
    Collaborative Innovation Centre for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China)

Abstract

The differential quadrature method (DQM) is a numerical technique widely applied in structure mechanics problems. In this work, a top-tensioned riser conveying fluid is considered. The governing equation of this riser under parametric excitations is deduced. Through Galerkin’s method, the partial differential governing equation with respect to time t and vertical coordinate z is reduced into a 1D differential equation with respect only to time. Moreover, the DQM is applied to discretize the governing equation to give solution schemes for the risers’ parametric vibration problem. Furthermore, the instability region of Mathieu equation is studied by both the DQM and the Floquet theory to verify the effectiveness of the DQM, and the solutions of both methods show good consistency. After that, the influences of some factors such as damping coefficient, internal flow velocity, and wet-weight coefficient on the parametric instability of a top-tensioned riser are discussed through investigating the instability regions solved by the DQM solution scheme. Hence, conclusions are obtained that the increase of damping coefficient will save the riser from parametric resonance while increasing internal flow velocity, or the wet-weight coefficient will deteriorate the parametric instability of the riser. Finally, the time-domain responses of several specific cases in both stable region and unstable region are presented.

Suggested Citation

  • Yang Zhang & Qiang Gui & Yuzheng Yang & Wei Li, 2022. "The Instability and Response Studies of a Top-Tensioned Riser under Parametric Excitations Using the Differential Quadrature Method," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1331-:d:795765
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    References listed on IDEAS

    as
    1. Constantin Bota & Bogdan Căruntu & Dumitru Ţucu & Marioara Lăpădat & Mădălina Sofia Paşca, 2020. "A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
    2. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. Yancheng Li & Sina Dang & Wei Li & Yingbin Chai, 2022. "Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
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