Year: 2012
Author: Chang Yi Wang, Wang Chien Ming
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 250–258
Abstract
In this paper, exact vibration frequencies of circular, annular and sector membranes with a radial power law density are presented for the first time. It is found that in general, the sequence of modes may not correspond to increasing azimuthal mode number $n$. The normalized frequency increases with the absolute value of the power index $|ν|$. For a circular membrane, the fundamental frequency occurs at $n = 0$ where $n$ is the number of nodal diameters. For an annular membrane, the frequency increases with respect to the inner radius $b$. When $b$ is close to one, the width $1 − b$ is the dominant factor and the differences in frequencies are small. For a sector membrane, $n − 1$ is the number of internal radial nodes and the fundamental frequency occurs at $n = 1$. Increased opening angle $β$ increases the frequency.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m1135
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 250–258
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Membrane vibration non-homogeneous exact circular annular sector.
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