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On the propagation of pressure transients in an elastic plate with a circular hole

Zur Ausbreitung von Druckverläufen in einer elastischen Platte mit Kreisloch

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Summary

In this report the problem studied is that of an infinite elastic plate which is being forced by a time varying pressure in a circular hole at its center. A two-dimensional theory is employed which predicts two of the infinite number of evanescent plate waves that are predicted by the exact three-dimensional theory. The solution is obtained in the frequency domain by means of integral transforms, and this solution is investigated numerically. Of greatest interest is the location of two pole type singularities at points just below the real frequency axis. These singularities, which are independent of the form of forcing, are the source of the edge resonance phenomenon that has been noted and reported in several places. The contribution of these singularities to the far field transient response is obtained by means of the method of steepest descent.

Zusammenfassung

Das in dieser Arbeit studierte Problem ist das einer unendlichen elastischen Platte, die durch einen im Innern eines Kreisloches angreifenden zeitlich veränderlichen Druck beansprucht wird. Angewendet wird eine zweidimensionale Theorie, die zwei der unendlich vielen, von der exakten dreidimensionalen Theorie vorhergesagten, langsam abklingenden Plattenwellen ergibt. Die mit Hilfe von Integraltransformationen im Frequenzbereich bestimmte Lösung wird numerisch untersucht. Von größtem Interesse ist die Lage zweier Pole knapp unterhalb der reellen Frequenzachse. Diese Singularitäten, die vom Verlauf der Belastung unabhängig sind, sind die Ursache der Erscheinung der Randresonanz, über die an verschiedenen Stellen berichtet wurde. Der Beitrag dieser Singularitäten zum Übergangsverhalten des Fernfeldes wird mit Hilfe der Methode des stärksten Abstieges bestimmt.

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  1. The Catholic University of America, Washington, D.C., USA

    J. J. McCoy

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  1. J. J. McCoy
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McCoy, J.J. On the propagation of pressure transients in an elastic plate with a circular hole. Acta Mechanica 11, 217–235 (1971). https://doi.org/10.1007/BF01176557

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  • DOI: https://doi.org/10.1007/BF01176557

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