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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 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.
}, 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 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.