The Eigenvalue Problem for Two-Dimensional Regions With Irregular Boundaries

[+] Author and Article Information
S. B. Roberts

Department of Engineering, University of California, Los Angeles, Calif.

J. Appl. Mech 34(3), 618-622 (Sep 01, 1967) (5 pages) doi:10.1115/1.3607752 History: Received January 03, 1967; Online September 14, 2011


A method for the construction of eigenfunctions for two-dimensional simply connected regions with irregular finite boundaries is presented. Solutions are obtained in the form of an eigenvalue power series which is shown to be uniformly convergent. The procedure is illustrated by application to the vibration problem of a class of thin membranes with epicycloidal boundary shapes.

Copyright © 1967 by ASME
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