On the Resistance and the Deflection of an Elastic Disk Moving Near a Plane Wall in a Viscous Fluid

Abstract

A force exerted on an elastic circular disk moving near a rigid wall in a viscous fluid and the deflection of the disk bent by the force are found analytically. The disk is clamped by the edge of a rigid hollow cylinder. The ratio of the distance from the wall to the radius of the disk and the ratio of the hydrodynamical force to the elastic force for the bending deflection are assumed to be small. The equations governing the motions of the disk and the viscous fluid are solved simultaneously in forms of a power series with respect to the two ratios. The force exerted on the disk is obtained up to the first order of each ratio and the deflection of the disk is determined up to the second order. When the distance from the wall is given as a function of time, the resistance and the deflection of the disk are concretely calculated.