Multistable dynamic behaviors of cantilevered curved pipes conveying fluid

Abstract

The present study newly found multistable dynamic characteristics of cantilevered curved pipes conveying fluid due to the gravity. These multistable behaviors of the pipe offer a promising avenue for the development and deployment of fluid actuators. Three configurations of curved pipes, namely, one-quarter circular, semi-circular, and three-quarter circular, are considered. A nonlinear dynamic theoretical model is established based on the geometrically exact model to investigate the large deformation behaviors of the curved pipe conveying subcritical fluid flows. The theoretical model for predicting large deformations of the curved pipe is validated through the finite element method (FEM). Afterwards, linear dynamic characteristics for three configurations of curved pipes are explored. Strangely, the discontinuity phenomenon for natural frequencies of the curved pipe occurs with increasing the flow velocity, which has never been reported before. Meanwhile, it is demonstrated that the gravity parameter has a significant effect on the critical velocity for flutter. Large deformation responses of the curved pipe in three configurations are further investigated, multistable dynamic behaviors are detected for all considered curved pipes. It displays that for different gravity parameters, the dynamic behavior of curved pipe is varying from a single state to multiple states with increasing the flow velocity. Results indicate that when the dimensionless gravity parameter and fluid velocity are 15 and 2.5, the curved pipe exhibits three distinct displacements due to static deformations. These three displacements are in three equilibrium states, which helps to explain the interesting phenomenon of frequency discontinuity.