Dynamic Behavior of Cracked Cantilevered Pipes Conveying Fluid

In this article, the effects of the non-propagating open cracks on the dynamic behaviors of a cantilevered pipe conveying fluid are studied. The model divides the pipe into a number of segments from the crack sections and assembles all segments each by each by a rotational spring which has no mass. The stiffness of the spring is obtained through linear fracture mechanics. In order to obtain the modal functions which satisfy the boundary conditions and geometrical discontinuity conditions at the crack’s location, a simple approach is used. That is adding polynomial functions to the modal functions of the uncracked beam. The equations of motion for the cracked cantilevered pipe conveying fluid is derived based on the extended Lagrange equations for systems containing non-material volumes. Not only the virtual work done by the discharged fluid, but also that done by the fluid at the crack position due to the geometrical discontinuity conditions are considered in the present equations of motion. In this article, several numerical examples are given. The comparisons of solutions of the present equations with that of model in existence show that the present work is better. The influences of the relative depth, the position ratio of the cracks, the flow velocity on the eigenvalues are depicted.