Investigation of the frequencies of in-plane modes of a thin circular singly clamped ring with application to Young's modulus determination

A simple theory based on the Rayleigh method is presented for the frequencies of the in-plane modes of a thin circular ring which is clamped at one point. The predictions of this theory are compared with experiment. A novel method for the determination of Young's modulus for material in the form of a ring is described; this method involves an extrapolation to the behaviour for the high-order modes and is not dependent on a full knowledge of the equation governing the vibration frequencies.