Flutter instability of supported pipes conveying fluid subjected to distributed follower forces

In the past decades, it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported. In this paper, the form of instability of supported pipes conveying fluid subjected to distributed follower forces is investigated. Based on the Pflüger column model, the equation of motion for supported pipes subjected concurrently to internal fluid flow and distributed follower forces is established. The analytical model, after Galerkin discretization to two degrees of freedom, is evaluated by analyzing the corresponding eigenvalue problem. The complex frequencies versus fluid velocity are obtained for various system parameters. The results show that either buckling or flutter instabilities could occur in supported fluid-conveying pipes under the action of distributed follower forces, depending on the parameter values of distributed follower forces.