Vibrations of free circular plates. Part 1: Normal modes

Abstract

The normal vibrating modes of free circular plates have been determined over an interval of more than six octaves, the solid-carbon-dioxide method of excitation being used to produce the nodal figures, and a valve oscillator to measure their frequencies. It is concluded that the nodal system of ideally uniform and entirely free plates would, in accordance with theory, consist only of circles, diameters and combinations of circles and diameters. It is found that although each simple mode has its characteristic frequency, cases occur in which the difference between two or even three of these is very small, and the number of nodal diameters, which as regards raising the pitch are approximately equivalent to one nodal circle, increases from two to five, in the interval investigated, in passing from figures with relatively more circles to those with relatively more diameters. The expression, based on approximate theory, for calculating the frequencies of the higher modes, in which it is assumed that the addition of two nodal diameters increases the frequency by as much as one nodal circle, is accordingly not applicable in ordinary practice. It is suggested that the simple and rapid solid-carbon-dioxide method of exciting free vibrations might be employed for testing the uniformity of plates, for detecting internal flaws, for studying recrystallization phenomena, and for obtaining comparative values of Poisson's ratio of metals and alloys.