Three-dimensional dynamics of supported pipe conveying fluid with arbitrary initial spatial shape

In order to meet different requirements of engineering applications, pipes conveying fluid usually have the geometric characteristic of a spatial initial shape. In this paper, a three-dimensional theoretical model based on absolute node coordinate formulation (ANCF) is proposed to analyze the dynamical behavior of spatial pipes conveying fluid with arbitrary initial shape. By introducing the spatial Frenet frame as the local coordinate, the global coordinate of each point on the pipe centerline is intuitively represented first. Considering the tensile, torsional and bending deformations of the pipe, the governing equations of spatial pipes conveying fluid are derived by means of the generalized Lagrange equation. Then the process of solving nonlinear static deformation, natural frequencies and nonlinear dynamic responses of the pipe is given. Further, by comparing the results calculated by the ANCF method with those of previous studies on straight and curved pipes, the effectiveness of the proposed three-dimensional ANCF model is verified. Finally, the nonlinear responses and natural frequencies of spatial pipes with three different initial shapes are calculated and some of them are compared with the results obtained using finite element simulations. The results show that the three-dimensional ANCF model proposed in this study has good feasibility and wide application prospect in nonlinear dynamics analysis of fluid-conveying pipes with complex initial shapes.