Abstract
Abstract The title problem constitutes a basic mathematical model where the separate or combined effects of possible manufacturing flaws are taken into account. These flaws are (a) deviations with respect to the ideal circular shape and (b) presence of a central inhomogeneity. The effects of these complicating factors on the fundamental frequency of a membrane are calculated using two approximate analytical techniques and the finite element method. Excellent agreement is shown to exist between the results obtained by the three different approaches.
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