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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1017–1032 | Cite as

Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

  • Demin ZhaoEmail author
  • Jianlin Liu
  • C. Q. Wu
Article

Abstract

The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to analyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.

Keywords

thermal load parameter excited local bifurcation unfolding parameter space physical parameter space 

Chinese Library Classification

O323 O326 O322 

2010 Mathematics Subject Classification

37G15 34E13 35Q74 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanics, College of Pipeline and Civil EngineeringChina University of PetroleumQingdao, Shandong ProvinceChina
  2. 2.Department of Mechanical and Manufacturing EngineeringUniversity of ManitobaWinnipeg MBCanada

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