Buckled behavior of a pipe conveying fluid subjected to unilateral point constraint

In this work, the buckled behavior of a pipe conveying fluid subjected to unilateral point constraint is investigated. The essentially nonlinear governing equation of the post-buckled state of a clamped-clamped pipe conveying fluid is formulated through the Euler–Bernoulli beam theory and the Hamilton principle, in which the essentially nonlinear natural of the governing equation is induced by unilateral point constraint. The first two critical velocities of fluid in pipe have been analytically determined. The contact force between the pipe and constrained point, and the constrained post-buckled state are obtained by using numerical method. Effects of the constraint point location, gap and the velocity of fluid on contact force and constrained post-buckled state of pipe are investigated. Results show that there are critical departure gap of constraint point and the velocity of fluid, and the snap-through of pipe can be observed for some given parameters, i.e. the pipe jumps from a constrained buckled state to a remote buckled state without constraint when the gap of constrained point or the velocity of fluid is in excess of it's critical departure gap or velocity.