Dynamic model of curved pipe conveying fluid based on the absolute nodal coordinate formulation

The dynamic model of the curved pipes conveying fluid, established by the generalized Hamiltonian principle, has been widely used to study the vibration properties of pipes with initial curve configurations. However, the results of these studies need to be validated by other modeling approaches. In this paper, a novel finite element model based on the absolute nodal coordinate formula (ANCF) is developed for curved pipes conveying fluid. The natural vibration of curved pipes is studied by using the proposed ANCF model. The natural frequencies and modes are compared with the results from the Hamiltonian model. A comparison of vibration modes shows slightly differences between the two models. Within a range of small curvature, the natural frequencies of the two models are highly consistent. However, as the increase of the curvature, the difference of the natural fre-quencies calculated by the two models gradually increases. The variation trends of the natural frequencies ob-tained by the two models become qualitatively different when the curvature over a certain value. In conclusion, this paper clarifies the conditions for the agreement between the Hamiltonian model and the proposed ANCF model. Meanwhile, it reveals that there may be a big difference between the two models in other situations without such conditions, which needs to be further studied.