Abstract
In numerous places in the literature of eigenvalue problems of mathematical physics one finds curves which approach each other and suddenly veer away. The author postulates that this ugly behavior may be the result of approximation in the representation of physical reality. In the present paper such behavior is demonstrated to arise from the application of the well-known Ritz-Galerkin method to the classical eigenvalue problem of the free vibration of a rectangular membrane.
Zusammenfassung
An vielen Stellen der Literatur über Eigenwertprobleme der mathematischen Physik kommen Kurven vor, die sich nähern, aber bevor sie sich schneiden, wieder auseinander laufen. Der Verfasser postuliert, dass dieses unschöne Verhalten durch die Approximation in der Erfassung der physikalischen Wirklichkeit verursacht werden kann. In der vorliegenden Arbeit wird als Beispiel die klassische Eigenwertaufgabe der schwingenden Rechteckmembrane gewählt und durch Anwendung des Verfahrens von Ritz-Galerkin ein derartiges Verhalten nachgewiesen.
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Ohio State University, Columbus, Ohio, USA
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Leissa, A.W. On a curve veering aberration. Journal of Applied Mathematics and Physics (ZAMP) 25, 99–111 (1974). https://doi.org/10.1007/BF01602113
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DOI: https://doi.org/10.1007/BF01602113