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.
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The Eigenvalue Problem for Two-Dimensional Regions With Irregular Boundaries
S. B. Roberts
Department of Engineering, University of California, Los Angeles, Calif.
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Roberts, S. B. (September 1, 1967). "The Eigenvalue Problem for Two-Dimensional Regions With Irregular Boundaries." ASME. J. Appl. Mech. September 1967; 34(3): 618–622. https://doi.org/10.1115/1.3607752
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