Volume 4, Issue 2
Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes

Chang Yi Wang and Wang Chien Ming

10.4208/aamm.10-m1135

Adv. Appl. Math. Mech., 4 (2012), pp. 250-258.

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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  |\nu|. For a circular   membrane, the fundamental frequency occurs  at n = 0 where n is the number of nodal  diameters. For an annular mem- brane,  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 \beta increases the frequency.

  • History

Published online: 2012-04

  • AMS Subject Headings

74.K15, 74.H45

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