Self excitations of slender structures under axial flow have been reported in a large variety of local flow configurations. This paper reports on the analytical results of a research program aimed at studying basic phenomena leading to fluidelastic instabilities.
A friction-based model is proposed to calculate the fluidelastic forces induced by axial flow. It is developed here for an axial flow between two surfaces. This method is an extension of the studies which were carried out by Miller (1970), Hobson (1982) and Mulcahy (1988). A pressure drop is introduced in the system with a local or continuous pressure drop factor. This model is based on a modal analysis and is presented for structures with several degrees-of-freedom.
The continuity and momentum equations are integrated along the fluid domain thickness with the boundary conditions on the structure. A linearization of these equations gives the expression of the fluctuating velocity and pressure. With a modal analysis, the fluidelastic force expression is obtained by the integration of the pressure on the structure wall. Three terms, called added terms, are identified: inertial, damping and stiffness. For several cases and different locations of the pressure drop, the behavior of this system and the flutter instability are analysed.