โ Scribed by A.M. Al-Jumaily; F.M. Najim
No coin nor oath required. For personal study only.
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 ecccentricity: smaller than 0โข6 the Rayleigh method reasonably estimates natural frequencies; larger than 0โข95 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.
๐ SIMILAR VOLUMES
This paper describes the method to analyze the free vibrations of simply supported cylindrical shells with an interior rectangular plate by using the receptance method. This method is based on the ratio of a de#ection (or slope) response to a harmonic force (or moment) at the joint. After "nding the