Three-dimensional dynamics of supported pipes conveying fluid

This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration (non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity, that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second- or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.