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Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes

Published online by Cambridge University Press:  03 June 2015

Chang Yi Wang  and
Wang Chien Ming
Chang Yi Wang*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Wang Chien Ming*
Affiliation:
Engineering Science Programme and Department of Civil and Environmental Engineering, National University of Singapore, Kent Ridge, Singapore 119260
*
Corresponding author. URL: http://www.eng.nus.edu.sg/civil/people/ceewcm/wcm.html, Email: cywang@math.msu.edu
Email: ceewcm@nus.edu.sg
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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 az-imuthal 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.

Keywords

74.K1574.H45Membranevibrationnon-homogeneousexactcircularannularsector
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 2 , April 2012 , pp. 250 - 258
Copyright
Copyright © Global-Science Press 2012

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References

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