Comparative Study of Frequencies for Plates Carrying Mass

Abstract

The present work is concerned with the determination of the fundamental frequencies of rectangular plates carrying a mass mounted at various positions. Although direct solution of the Navier and Lévy methods is not generally practical, an energy method involving double trigonometric functions was developed to obtain approximate closed‐form solutions. A finite element analysis is also presented for comparison. Extensive experimental investigation on the three plates through a shaker system was conducted to collect useful test data. Comparisons of experimental results with theoretical predictions of the finite element and energy methods are made. The results confirm that the frequency of the plate decreases as the weight of the component mass is increased, and the frequency increases as the mass moves away from the center of the plate. The work suggested that the tested plates can be approximately represented by plates with two opposite edges simply supported and the other two edges clamped (SCSC) boundary conditions. A set of comparisons also reveals that there is a need for improvement in the analytical methods for heavier masses.