Static equilibrium configuration and nonlinear dynamics of slightly curved cantilevered pipe conveying fluid

Abstract

In engineering applications, fluid-conveying pipes usually have geometric imperfections or initially curved configurations. Unlike the initially curved pipe supported at both ends, a slightly curved cantilevered pipe is capable of displaying some interesting behavior because it is a nonconservative system of fluid-structure interactions. In the present study, nonlinear static and dynamic behaviors of cantilevered pipes conveying fluid are explored, with four different initial shapes being considered. To this end, the strongly nonlinear governing equation is derived by employing the extended Lagrange equations written for dynamical systems containing non-material volumes. The static (steady) equilibrium configurations, stability, and nonlinear dynamics of the slightly curved cantilevered pipes are obtained with the aid of absolute nodal coordinate formulation (ANCF). Based on extensive numerical calculations, some interesting and sometimes unexpected results are displayed. The first unexpected feature in this dynamical system is that the flow-induced static deformation of the pipe can be extremely large even if the initial geometric imperfection of the pipe is quite small. The second unexpected result is that the critical flow velocity for flutter instability of the slightly curved pipe conveying fluid may be either lower or higher than that of a straight pipe, mainly depending on the static equilibrium configuration when the critical flow velocity is just reached. Moreover, it is demonstrated that the slightly curved pipe oscillates about the static equilibrium position instead of the initially curved centerline, and the preferred form of post-instability behavior is periodic motion within a wide range of system parameters considered.