AN APPROXIMATION TO THE VIBRATIONS OF OBLATE SPHEROIDAL SHELLS

Abstract

This paper presents the results of investigating the axi-symmetric free vibrations of an isotropic thin oblate spheroidal shell. An oblate spheroid is considered as a continuous system constructed from two spherical shell caps by matching the continuous boundary conditions. This approximation technique is used to express the results in a continuous function analytical formation. The radii and opening angles of the spherical elements are chosen according to the eccentricity of the oblate spheroid.It is shown that for an eccentricity: smaller than 0·6 the Rayleigh method reasonably estimates natural frequencies; larger than 0·95 both of the shallow and non-shallow spherical shell theories predict natural frequencies in close agreement; and equal to zero an exact thin sphere solution emerges.The method presented herein is clearly an engineering approximation for special purpose shells and does not require the computer storage of numerical methods. Also, it may be quite useful when utilised judiciously in many applications, such as in force response analysis. Comparison is made between the present technique, the Rayleigh method, and experimental data for two laboratory models. The formulation can be extended to many types of oblate spheroids with different support conditions and still retain the functional representation.