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Eigenfrequencies of an elliptic membrane


Authors: B. A. Troesch and H. R. Troesch
Journal: Math. Comp. 27 (1973), 755-765
MSC: Primary 73.65
DOI: https://doi.org/10.1090/S0025-5718-1973-0421276-2
MathSciNet review: 0421276
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Abstract: The first few eigenfrequencies of a homogeneous elliptic membrane, which is fixed along its boundary, are given in a graph. It is explained in detail, how more accurate results can readily be obtained for special purposes. The known expansion of the eigenfrequencies for small and large eccentricities are summarized. As an application some nodal patterns for a membrane with a double eigenvalue are presented.


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DOI: https://doi.org/10.1090/S0025-5718-1973-0421276-2
Keywords: Linear membrane vibrations, Mathieu functions, Helmholtz equation in elliptic coordinates
Article copyright: © Copyright 1973 American Mathematical Society

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