Three-dimensional dynamic model of the curved pipe based on the absolute nodal coordinate formulation

Abstract

Due to the lack of advanced models and analytical methods, the study of pipe conveying fluid usually only considers the in-plane vibration of straight pipe. In order to fully understand the dynamic characteristics of curved pipe, it is necessary to establish the three-dimensional (3D) dynamic model. However, there are still few 3D modeling methods for the curved pipe. In this paper, based on the absolute nodal coordinate formulation (ANCF), a 3D finite element model for the curved pipe is developed. The nonlinear dynamic equations of the pipe system are derived by using the extended Lagrange equations. The natural frequencies and modes are calculated by linearizing the equations. The established model and the adopted method are verified through the comparison with relevant literature and ANSYS simulation. Furthermore, the effects of the relevant parameters on the natural vibration of curved pipe are discussed. The in-plane and out-of-plane natural vibration characteristics of curved pipe are compared and summarized for the first time. Finally, the advantages of the proposed model are outlined by the comparison with the planar dynamic model. The results provide new information about the effect of initial curvatures on the spatial vibration characteristics of pipes. In conclusion, this paper provides a novel dynamic model for studying the spatial vibration of the curved pipe. In the meantime, the results of this paper can also can guide for the research of the vibration of curved pipes in engineering.