Wave Motions on a Circular Membrane and in a Circular Water Tank due to an Unsteady Rotating External Force

Abstract

Wave motions on a circular membrane and in a circular water tank due to an unsteady rotating external force are discussed. The response function and the condition of resonance are derived. In the case of a constant rotating force, the resonance is observed when the angular velocity of the rotating force coincides with any of the phase angular velocities of the rotating free waves on a circular membrane or in a water tank. The above mentioned wave motions may in a sense be considered to be similar to the wave phenomena observed on a disk of a rotating machine such as a centrifugal compressor, on a tyre of an automobile and on an ocean as tidal wave etc., from a mathematical point of view.