EXTENSIONAL AXI-SYMMETRIC SECOND CLASS VIBRATIONS OF A PROLATE SPHEROIDAL SHELL
Abstract
The differential equations for the mode shapes are derived, by application of Hamilton's principle, in prolate spheroidal coordinates. In the extensional approximation that axi-symmetric modes separate into two classes. The equations for second class vibrations, with displacements in the meridian planes, do not allow a closed form solution. The displacements are expanded in series of spheroidal angle functions, chosen such that in the limit of the spherical shell one term in each series goes to the corresponding exact solution. Approximations to the frequency parameters and mode shapes are obtained with the Rayleigh-Ritz method, using terms of these series. The plot of the frequency parameter for the breathing mode as a function of the eccentricity varies continuously between the known values for the spherical and the infinite cylindrical shell. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1961
- Accession Number
- AD0254122
Entities
People
- Alexander Silbiger
- Frank L. Dimaggio
Organizations
- Columbia University