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The purpose of this paper is to investigate the linear vibrations of an elastic plate subject to irrotational, incompressible fluid flow bounded by a rigid cylinder.

The plate is placed diametrically in the cylinder and extends along it, both infinite in length. The fluid flow is in the axial direction of the cylinder.

The problem is solved analytically and the eigenfrequencies are obtained explicitly.

The solution offered in this paper allows investigation of the instabilities and computation of the flutter velocity/minimum flow velocity at which the plate vibrations grow in time.

Investigate the vibrations of the walls of a rectangular channel through which fluid flows.

Analytical solution of linearised compressible potential flow equations for the fluid coupled with the plate vibration equations for two opposing walls of the channel.

An expression for the flutter velocity of the fluid in the channel at which unstable oscillations of the channel walls first occurs is developed.

The computation of flutter velocity for a rectangular duct is of interest to a variety of industrial fields.

The analytical solution derived is original.