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Approximate determination of vibration frequencies of doubly connected membranes of complicated boundary shape

✍ Scribed by V.H. Cortinez; P.A.A. Laura; H.C. Sanzi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 434 KB
Volume: 48
Category: Article
ISSN: 0003-682X
DOI: 10.1016/0003-682x(96)00005-9

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✦ Synopsis

This paper deals with the determination of upper bounds of vibration frequencies of doubly connected membranes fixed at both boundaries by means of a conformal mapping approach.

If the exact Laurent series which maps the given domain onto a circular annulus in the transformed domain is not known, it is shown that for certain cases of practical interest one can still obtain an approximate value of the frequency, not necessarily being an upper bound. The numerical values obtained in the present investigation are in good agreement with those determined by means of (a) an extended Pnueli's method and (b) a$nite element code.

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