Accession Number:

AD0254122

Title:

EXTENSIONAL AXI-SYMMETRIC SECOND CLASS VIBRATIONS OF A PROLATE SPHEROIDAL SHELL

Descriptive Note:

Corporate Author:

COLUMBIA UNIV NEW YORK INST OF FLIGHT STRUCTURES

Report Date:

1961-02-01

Pagination or Media Count:

1.0

Abstract:

The differential equations for the mode shapes are derived, by application of Hamiltons 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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE