Vibrations of an anisotropic plate under fluid flow in a channel

Abstract

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 indefinitely; 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.