Motion of a Viscous Liquid Layer Covered by a Thin Plate Subject to Gas Stream

Abstract

Motion of a horizontal viscous liquid layer under the action of the gravity covered by an elastic thin plate subjected to gas stream is studied. Also, the nonlinear terms in the governing equations for the fluid and the elastic plate are taken into account. The wavelength of a deformed elastic plate is assumed to be very large compared with the depth of the viscous liquid layer. An evolutional equation governing the disturbance of the elastic plate is obtained to an accuracy of the fourth order of small parameters, the wave number and the amplitude. The equation is solved analytically and the neutral stability curves are obtained . It is found that there is an equilibrium state in the linearly unstable region for the wave number. The amplitude of the elastic plate in the equilibrium state is obtained as a function of Reynolds number of the liquid layer, the bending stiffness, Young's modulus, the in-plane force of the plate, and the velocity of the gas stream. It is not a function of the initial disturbance.