Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid?

The effect of the elastic Winkler and rotatory foundations on the stability of a pipe conveying fluid is investigated in this paper. Both elastic foundations are partially attached to the pipe. Ii turns out that the single foundation, either translational or rotatory which is attached to the pipe along its entire length, increases the critical velocity. Such an intuitively anticipated strengthening effect is surprisingly missing for the elastic column on Winkler foundation subjected to the so-called statically applied follower forces. Yet, partial foundation for the pipe conveying fluid is associated with a nonmonotonous dependence of the critical velocity versus the attachment ratio defined as the length of the partial foundation over the entire length of the pipe. It is concluded that such a paradoxical nonmonotonicity is shared by both the realistic structure (pipe conveying fluid) and in the "imagined system, " to use the terminology of Herrmann pertaining to the column under to follower forces.