Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes

Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes

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.

Author Details

Chang Yi Wang

Wang Chien Ming

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