This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

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