Three-dimensional dynamical model for cantilevered pipes conveying fluid under large deformation

Abstract

The present work is devoted to providing a full version of theoretical model for three-dimensional (3D) oscillations of a cantilevered pipe conveying fluid under large deformation. The geometric nonlinearity of the pipe is exactly considered by using an exact expression for the curvature of the pipe centerline. By taking variation operations with translational displacements or bending angles as the variables, two types of geometrically exact (GE) governing equations are derived and they are demonstrated to be equivalent. By using Taylor expansion (TE), the derived GE equations can degenerate into the previous version of governing equations based on a small-amplitude assumption. Analyses of the stability and nonlinear vibrations are conducted by means of both GE and TE models. As expected, the results of the pipe’s stability and small-amplitude oscillations predicted by using the TE model agree well with the counterpart predicted by the GE model. When the vibration amplitude of the pipe becomes large, however, remarkable difference can be found between the results obtained by using the TE and GE models. Besides, in some cases, the large-amplitude oscillations of the pipe predicted by the TE model may be unrealistic. Therefore, the newly developed GE model is more reliable for evaluating the 3D motions of cantilevered pipes conveying fluid under large deformation.