On the Transverse Vibration of an Elliptic Plate with Clamped Edge

Abstract

The transverse vibration of a uniform thin elliptic plate with clamped edge is solved in an exact manner by the use of Mathieu functions and modified Mathieu functions. The relationship between the frequency of the fundamental mode of vibration and the eccentricity of the elliptic plate is shown graphically. Also, an approximate formula for the said relationship is derived correct to the fourth power of the eccentricity, which may be adequately used in case when the eccentricity is not so large.