Vibration of Annular Mindlin Plates with Small Cores

In most publications on vibration of annular plates, the natural frequencies are only presented for inner radius as small as one-tenth of its outer radius, but there are hardly any results presented for cores smaller than this inner radius value. This is attributed to severe scaling problems upon using numerical techniques to obtain the fundamental frequency of plates when the inner radius becomes very small. This study aims to solve this class of plate vibration problem where the annular plates are thick and their core radii are much less than one-tenth of the outer radius. The analysis involved using the Mindlin plate theory so as to allow for the effects of transverse shear deformation and rotary inertia and the truncation of the terms in the Bessel functions defining the characteristic equations in order to overcome the scaling problem. Eventually, the fundamental frequency of a thick annular plate could be deduced as finite or zero when the inner radius approaches zero.