Abstract
Saint-Venant’s method to solve the Poisson equation is applied to the Helmholtz equation which governs membrane vibration. A family of non-circular membrane shapes with N-fold rotational symmetry is presented. Membrane shapes, properties, and fundamental frequencies are tabulated. The solutions are exact and can serve as accuracy standards for approximate methods.
Issue Section:
Technical Brief
References
1.
Wang
, C. Y.
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, C. M.
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Wang
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, “Fundamental Frequencies of Rounded Polygonal Membranes— A Class of Homotopy Shapes
,” ASME J. Vib. Acoust.
, 135
(1
), p. 014501
. Copyright © 2022 by ASME
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