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The purpose of this paper is to analyse analytically a control scheme in which the resonance frequencies of a rectangular plate is modified by applying a discrete lateral force proportional to the displacement of the plate measured at a single point.

An isotropic, elastic, rectangular, thin plate which is simply supported along all sides is actuated at point (x₂, y₂) by applying a force, and the displacement is measured at (x₁, y₁).

The main outcome is the full analytical solution for the controlled eigenfrequencies and mode shapes which allows a detailed study of the efficiency of the control method proposed.

The present study was made in the form of an exact analytical solution and demonstrates that it is possible to affect the eigenfrequencies and mode shapes of a plate by measuring the displacement and applying a pressure at discrete points on the plate.

The aeroelastic stability of an orthotropic panel in a duct with rectangular cross section is examined. The panel extends along the flow direction in the duct which is infinite in length. The panel vibration is modeled by linear plate theory and the flow in the duct is modeled by the compressible linearized potential theory. The panel is placed in the mid‐section of the duct and is simply supported at the sides. The material of the panel is assumed to be orthotropic. This would model, for example, unidirectional fibers placed in an isotropic plate, either along or perpendicular to the flow direction. An analytical solution is given for the eigenvalues of the panel vibration and results are presented for a range of parameters in the problem.