Eigenfrequencies of an Elliptic Membrane

DOI10.2307/2005509zbMath0271.35017OpenAlexW4252659277MaRDI QIDQ3215648

B. Andreas Troesch, Hans R. Troesch

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/2005509

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Membranes (74K15) Modal analysis in linear vibration theory (70J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût, Computing elliptic membrane high frequencies by Mathieu and Galerkin methods, Spectral collocation solutions to multiparameter Mathieu's system, Analytical and numerical investigation for true and spurious eigensolutions of an elliptical membrane using the real-part dual BIEM/BEM, Sharp stability of some spectral inequalities, Analytical investigation for true and spurious eigensolutions of multiply-connected membranes containing elliptical boundaries using the dual BIEM, The energetics of flow through a rapidly oscillating tube. Part 2. Application to an elliptical tube, Quasi-analytical solution of two-dimensional Helmholtz equation, Elliptical Membranes with Smallest Second Eigenvalue, The local geometry of chaotic billiards, High-accuracy calculation of eigenvalues of the Laplacian in an ellipse (with Neumann boundary condition)

Cites Work

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• Generation of Bessel Functions on High Speed Computers
• Tables of Values of the Modified Mathieu Functions
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• THE PRINCIPAL FREQUENCIES OF VIBRATING SYSTEMS WITH ELLIPTIC BOUNDARIES