A Theory for the Vibratory Effects Produced by a Propeller on a Large Plate

The flow generated on an infinite plane or wall by a single-bladed ship propeller rotating on a shaft parallel to the plane in a uniform superposed stream is first considered. After demonstrating that the pressure on the wall depends only on blade position and not upon the time-rate-of-change of blade position, the force and the moment on the plane about a transverse axis are computed and found to be given by very simple formulas. Under the assumed neglect of the interferences arising from the image of the propeller in the wall, it is shown that the net force and moment on the wall are zero for all lightly loaded propellers having two or more blades. The case of nonuniform inflow is considered and shown to give nonzero vibratory forces. The case of uniform inflow is still of interest because the zero force and moment result does not mean that an elastic wall would not vibrate, and to substantiate this, a formula for the deflections of a thin "infinite" plate is given. This formula has not been evaluated because of its complexity. It is recommended that numerical evaluation be undertaken through the use of a high-speed computer.