No abstract

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.

An analytical solution is given for the eigenfrequencies of the vibrations of a generally orthotropic plate placed in a rigid channel of rectangular cross section through which fluid flows. The fluid flow, assumed to be inviscid, compressible and non-steady, is modeled using a linearized potential equation. The plate is simply supported along the channel and extends indefinitely1 its vibrations are also assumed to be linear. The resulting system of partial differential equations are simplified assuming a travelling wave mode along the plate. The problem is reduced to a single integro-differential equation and solved analytically to obtain an algebraic eigenvalue equation relating travelling wavespeed to wavelength and the velocity of fluid flow. It is found that, for the case of a composite plate within a duct, placing the strengthening fibers perpendicular to flow direction increases the minimum velocity at which the unstable oscillations will occur in most cases.

Vibration characteristics of an elastic plate in the shape of an infinite strip are changed by applying a lateral concentrated force to the plate. The homogeneous, isotropic, elastic plate is infinite in the x-direction and the sides are simply supported. The size of the force is changed in proportion to the displacement measured at a certain point of the plate. The proportionality constant serves as the control parameter. The mathematical formulation of this distributed control problem and its analytical solution in terms of the vibration frequencies of the plate are given. The vibration frequencies are plotted as a function of the control parameter.

PurposeThe 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.Design/methodology/approachAn 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).FindingsThe 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.Originality/valueThe 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.