Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

doi:10.1007/s10483-020-2557-9

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (1): 15-32.doi: https://doi.org/10.1007/s10483-020-2557-9

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

Tianli JIANG^1,2, Huliang DAI^1,2, Kun ZHOU^1,2, Lin WANG^1,2

1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China

收稿日期:2019-05-15 修回日期:2019-07-24 发布日期:2019-12-14
通讯作者: Lin WANG E-mail:wanglindds@hust.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11622216, 11602090, and 11672115), the Natural Science Foundation of Hubei Province (No. 2017CFB429), and the fundamental Research Funds for the Central Universities of China (No. 2017KFYXJJ135)

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

Tianli JIANG^1,2, Huliang DAI^1,2, Kun ZHOU^1,2, Lin WANG^1,2

1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China

Received:2019-05-15 Revised:2019-07-24 Published:2019-12-14
Contact: Lin WANG E-mail:wanglindds@hust.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11622216, 11602090, and 11672115), the Natural Science Foundation of Hubei Province (No. 2017CFB429), and the fundamental Research Funds for the Central Universities of China (No. 2017KFYXJJ135)

摘要/Abstract

摘要： In this study, the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional (3D) theoretical model. The complete nonlinear governing equations are discretized via Galerkin's method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm. Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions. A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio, the flow velocity, and the gravity parameter on the post-buckling behavior of the pipe. Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter. It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached. Just beyond the critical flow velocity, the pipe would lose stability by static divergence via a pitchfork bifurcation, and two possible nonzero equilibrium positions are generated. It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter. Unlike a pipe with two immovable ends, however, the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors. The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity. In addition, the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.

关键词: fluid-conveying pipe, axially sliding downstream end, nonplanar, postbuckling behavior

Abstract: In this study, the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional (3D) theoretical model. The complete nonlinear governing equations are discretized via Galerkin's method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm. Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions. A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio, the flow velocity, and the gravity parameter on the post-buckling behavior of the pipe. Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter. It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached. Just beyond the critical flow velocity, the pipe would lose stability by static divergence via a pitchfork bifurcation, and two possible nonzero equilibrium positions are generated. It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter. Unlike a pipe with two immovable ends, however, the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors. The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity. In addition, the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.

Key words: fluid-conveying pipe, axially sliding downstream end, nonplanar, postbuckling behavior

中图分类号:

74F10

Tianli JIANG, Huliang DAI, Kun ZHOU, Lin WANG. Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 15-32.

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Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

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