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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} }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.