Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

• Published in: Applied mathematics and mechanics Vol. 36; no. 6; pp. 729 - 746
• Main Authors: Gan, Chunbiao, Jing, Shuai, Yang, Shixi, Lei, Hua
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.06.2015; The State Key Laboratory of Fluid Power Transmission and Control,School of Mechanical Engineering,Zhejiang University,Hangzhou 310027,China%Department of Engineering Mechanics,Zhejiang University,Hangzhou 310027,China
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; 分岔角; 悬挂系统; 悬臂; 流体动力学; 混沌运动; 稳定性; 管道输送; 输液管; 70K50; 74H45; cantilevered pipe conveying fluid; supported angle; dynamical bifurcation; modal analysis; TH113; response characteristics
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-015-1946-6

The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system （H-S） and standing system （S-S） are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.