In-plane and out-of-plane dynamics of curved pipes conveying fluid by integral transform method

  • Fangqiu Li
  • Chen AnEmail author
  • Menglan Duan
  • Jian Su


This study presents a new solution for the dynamic behavior of in-plane and out-of-plane motion of a curved pipe conveying fluid, using the generalized integral transform technique (GITT). The system of sixth- and fourth-order partial differential equations governing three-dimensional motion of the curved pipe is integral transformed into three coupled systems of second-order ordinary differential equations, which are solved numerically by using the NDSolve routine of Mathematica. Excellent convergence behavior of the GITT solution is shown by comparing the vibration deflections at different points along the curved pipe centerline obtained with of different truncation orders. The results of natural frequencies and vibration responses compare well with available results in the literature obtained by other methods. Furthermore, we investigate the dynamic behavior of the curved pipe with different axial forces, flow velocities and other vibration parameters. A relationship between boundary conditions and axial forces is provided, and a series of vibration displacement and velocity trajectories is obtained. It is shown that the GITT is a convenient and effective mathematical method for vibration analysis of the curved pipe conveying fluid and can be used for further study of the dynamics of variable-curvature curved pipes.


Curved pipe conveying fluid Generalized integral transform technique Dynamic behavior In-plane and out-of-plane vibration Natural frequency 



The work was supported by National Key Research and Development Plan (Grant No. 2016YFC0303704), National Natural Science Foundation of China (Grant Nos. 51509258 and 51879271), the 111 Project (B18054), and CNPq and FAPERJ of Brazil.

Compliance with ethical standards

Conflict of interest

We have no conflict of interest to declare.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.College of Safety and Ocean EngineeringChina University of Petroleum-BeijingBeijingChina
  2. 2.Nuclear Engineering ProgramCOPPE, Universidade Federal do Rio de JaneiroRio de JaneiroBrazil

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