Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes
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.
