On the Vibrations of Parabolic Membranes

[+] Author and Article Information
L. L. Fontenot, D. O. Lomen

General Dynamics/Astronautics; San Diego State College, San Diego, Calif.

J. Eng. Ind 88(1), 45-50 (Feb 01, 1966) (6 pages) doi:10.1115/1.3670889 History: Received December 15, 1964; Online December 08, 2011


This study is concerned with the transverse vibrations of a theoretical membrane which occupies a region bounded by two confocal parabolas. The eigenvalues and eigenfunctions for Dirichlet conditions are determined. Nodal patterns for the free vibrations of the membrane are given for various forms of symmetry. Orthogonality relations are established; initial value problems and forced vibrations also are considered.

Copyright © 1966 by ASME
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