FEM formulation for dynamic instability of fluid-conveying pipe on non-uniform elastic foundation

In this study, we investigate the effect of a nonuniform inkler-type elastic foundation on the stability of pipes conveying fluid fixed at the upstream end only. A stability analysis of transverse motion aims at determining the flutter velocity as a function of the governing control parameters such as fluid mass over the pipe mass ratio, or foundation stiffness. The global stability of the system is analyzed applying an ad-hoc developed finite-element formulation that leads to a discrete state-space equation of motion. It is shown that for a uniform foundation, an increased stiffness of the Winkler coefficient leads to an increased critical flow speed for any value fluid/pipe mass ratio, while in the case of a nonuniform elastic foundation, the system may present higher or lower critical flow speed depending on the fluid/pipe mass ratio. Special attention is paid to the “S” type behavior of the instability curves, as reported in numerous papers.