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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.

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 aim of this study is to modify the critical Reynolds number (Re_cr) which is the critical parameter of the transition from laminar to turbulence regime. The transition to turbulence is delayed by increasing the critical Reynolds number.

A method to control the critical Reynolds number of viscous flow between parallel plates with an imposed pressure gradient to infinitesimal harmonic disturbances is introduced. The method consists of introducing harmonic perturbations to the lower plate based on skin friction measurements at the upper plate. The size of the introduced harmonic perturbation is chosen to be proportional to the measured skin friction. The proportionality constant is the control parameter for the manipulation of the critical Reynolds number. The resulting eigenvalue problem, similar to the Orr‐Sommerfeld problem, is solved for various values of the control parameter.

Solution of the eigenvalue problem shows that the critical Reynolds number for the instability with respect to infinitesimal disturbances can be increased from 5,772.22 to 37,900.

The paper demonstrates that it is theoretically possible to increase the critical Reynolds number of parallel plate flow from 5,772.22 to 37,900 by applying a small motion to the bottom plate, the amplitude of the motion being proportional to the skin friction measured at the upper 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.

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.