Forced Vibration of Internally Damped Circular Plates with Supported and Free Boundaries

Abstract

This paper considers the vibration response of circular plates that are driven at their midpoints by a sinusoidally varying point force. The plates have simply supported or free boundaries and are assumed to be internally damped. The corresponding solutions to the thin-plate wave equation are described. Because the solutions involve ordinary and modified Bessel functions of complex argument, methods for obtaining the real and the imaginary parts of these functions are described and their results compared. Expressions are derived for the driving-point and transfer impedances and for the force and displacement transmissibilities of the plates. Representative calculations showing the frequency dependence of these quantities for internal plate damping of the solid type are presented, and their physical significance is discussed. The effect of attaching lumped masses to the plates at their midpoints is also examined.