Vibrations of a Clamped Circular Plate Carrying Concentrated Mass

Abstract

Abstract The vibrations of a circular plate clamped at its edge and carrying a concentrated mass at its center are considered. The plate is excited by a motion of the framing, assumed rigid, to which it is clamped. The first four natural frequencies are displayed graphically as functions of mass ratio, and are calculated more precisely for μ = 0, μ = 0.05, and μ = 0.10. The motions of two subsystems with one degree of freedom are compared, one subsystem being driven by the framing and the other by the concentrated mass on the plate. The plate-mounted subsystem has a response in excess of the response of the framing-mounted subsystem if the framing is suddenly put into motion with constant velocity. Except in the neighborhood of their peaks, whose locations depend upon mass ratio, the subsystem resonance curves are depressed in height by increasing the mass ratio.