Stability of an elastic supported flat plate subjected to potential flow

Abstract

In this paper we investigated the dynamics of a thin, flat plate placed in potential planar flow and attached by springs to the wall. %The length of %the plate in the direction perpendicular to the plane of flow was considered %to be infinite. Furthermore, the centre of gravity of the plate was assumed to move only perpendicular to the direction of the flow. Thus, a two-degree-of-freedom oscillatory system was analysed, whose natural frequencies depend on the flow velocity. The equations of motion were derived for two cases: first, the flow forces acting on the plate were determined using a quasi-steady approach; in the second case, we used the formulas derived by Theodorsen assuming unsteady potential flow. Finally, we obtained and compared the stability charts for the two cases.