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

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

Published online: 2012-04

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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.

• Keywords

Membrane vibration non-homogeneous exact circular annular sector

74.K15 74.H45

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@Article{AAMM-4-250, author = {Chang Yi Wang and Wang Chien Ming}, title = {Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {2}, pages = {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 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1135}, url = {http://global-sci.org/intro/article_detail/aamm/118.html} }
TY - JOUR T1 - Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes AU - Chang Yi Wang & Wang Chien Ming JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 250 EP - 258 PY - 2012 DA - 2012/04 SN - 4 DO - http://dor.org/10.4208/aamm.10-m1135 UR - https://global-sci.org/intro/aamm/118.html KW - Membrane KW - vibration KW - non-homogeneous KW - exact KW - circular KW - annular KW - sector AB -

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.

Chang Yi Wang & Wang Chien Ming. (1970). Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes. Advances in Applied Mathematics and Mechanics. 4 (2). 250-258. doi:10.4208/aamm.10-m1135
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