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

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...

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Bibliographic Details
Published in:Applied acoustics 1996-08, Vol.48 (4), p.301-309
Main Authors: Cortinez, V.H., Laura, P.A.A., Sanzi, H.C.
Format: Article
Language:English
Subjects:
conformal mapping
finite element
Laurent series
Pnueli's method
Upper bounds
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Summary: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 finite element code.
ISSN:0003-682X
1872-910X
DOI:10.1016/0003-682X(96)00005-9