Axisymmetric Free Vibration of Thin Prolate Spheroidal Shells


In this paper a detailed study of the theory of free axisymmetric vibration of thin isotropic prolate spheroidal shells is presented. The analysis is performed according to Rayleigh – Ritz method. This method as well as an approximate modeling technique were attempted to estimate the natural frequencies for the shell. This technique is based on considering the prolate spheroidal as a continuous system constructed from two spherical shell elements matched at the continuous boundaries. Through out the obtained results it is found that this method predicted fairly well the natural frequencies of a prolate spheroidal shell for all values of eccentricities.