Acta Mechanica Sinica

, Volume 35, Issue 6, pp 1241–1256 | Cite as

Nonplanar flow-induced vibrations of a cantilevered PIP structure system concurrently subjected to internal and cross flows

  • Z. Y. Liu
  • T. L. Jiang
  • L. WangEmail author
  • H. L. Dai
Research Paper


Pipe-in-pipe (PIP) structures are widely used in offshore oil and gas pipelines to settle thermal insulation issues. A PIP structure system usually consists of two concentric pipes and one softer layer for thermal insulation consideration. The total response of the system is related to the dynamics of both pipes and the interactions between these two concentric pipes. In the current work, a theoretical model for flow-induced vibrations of a PIP structure system is proposed and analyzed in the presence of an internal axial flow and an external cross flow. The interactions between the two pipes are modeled by a linear distributed damper, a linear distributed spring and a nonlinear distributed spring along the pipe length. The unsteady hydrodynamic forces due to cross flow are modeled by two distributed van der Pol wake oscillators. The nonlinear partial differential equations for the two pipes and the wake are further discretized by the aid of Galerkin’s technique, resulting in a set of ordinary differential equations. These ordinary differential equations are further numerically solved by using a fourth-order Runge–Kutta integration algorithm. Phase portraits, bifurcation diagrams, an Argand diagram and oscillation shape diagrams are plotted, showing the existence of a lock-in phenomenon and figure-of-eight trajectory. The PIP system subjected to cross flow displays some interesting dynamical behaviors different from that of a single-pipe structure.


Cantilevered PIP structure Theoretical model Flow-induced vibration Cross flow Internal flow 



The work was supported by the National Natural Science Foundation of China (Grant 11622216).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Z. Y. Liu
    • 1
    • 2
  • T. L. Jiang
    • 1
    • 2
  • L. Wang
    • 1
    • 2
    Email author
  • H. L. Dai
    • 1
    • 2
  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina

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