An out-of-plane vibration model for in-plane curved pipes conveying fluid

Vibration characteristics of curved pipes conveying fluid have been studied extensively. However, most researches are limited to the in-plane transverse vibration. There is still a lack of effective modeling and corresponding research for the out-of-plane vibration of an in-plane curved pipe. For this purpose, a dynamic model of out-of-plane vibration of an in-plane curved pipe conveying fluid is established for the first time. Based on the force analysis of the pipe and the fluid, the governing equations of the out-of-plane vibration are derived analytically. By the transformation of arc length coordinates and global coordinates, a new description of the out-of-plane vibration of bending and torsion is introduced. The critical velocity, natural frequencies and modes of the curved pipe are calculated based on the Galerkin truncation method. The results show that the pipe with larger in-plane curvature has lower critical velocity of out-of-plane motion. Furthermore, there is a significant decrease in the natural frequencies with the increase of curvature and fluid velocity. In conclusion, this paper provides a new dynamic model for studying the out-of-plane vibration of in-plane curved pipes. Meanwhile, the dynamic characteristics of the out-of-plane vibration of the curved pipe are also revealed for the first time. [Display omitted] •A dynamic model for out-of-plane vibration of an in-plane curved pipe is developed.•The out-of-plane bending-torsion coupling vibration of curved pipe is described.•Effects of initial curvature and flow velocity on out-of-plane vibration is revealed.•Natural frequencies of the pipe may decrease significantly as the curvature changes.