@Article{AAMM-4-2,
author = {Yi, Wang, Chang and Wang, Ming, Chien},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m1135},
url = {https://global-sci.com/article/73541/exact-vibration-solutions-of-nonhomogeneous-circular-annular-and-sector-membranes}
}