Dynamics of simply supported fluid-conveying pipes with geometric imperfections

In this paper, the dynamics of simply supported fluid-conveying pipes with geometric imperfections is examined, by considering the integral–partial–differential equation of motion. The effect of sinusoidal wave or parabolic variations of imperfections is investigated for the four-degree-of-freedom (N=4) model of the system. Linear analysis shows that each type of imperfections affects the natural frequency of only one single mode. For half-sinusoidal wave or parabolic variation of imperfections, the critical flow velocity at which buckling instability occurs is higher than that for a pipe without imperfections. In all cases, the pipe remains in its undeformed static equilibrium state at low flow velocity. At high flow velocity; however, nonlinear analysis predicts that the pipe would be attracted to one of two other nontrivial equilibria, which, more importantly, may be asymmetric due to the presence of imperfections. For pipes with imperfection in the form of half-sinusoidal wave or parabolic variation, interestingly, the nonlinear theory predicts that a small buckling displacement would occur at flow velocities slightly lower than the critical flow velocity predicted by the linear theory.