Radial vibration and equivalent circuit of thin elastic circular rings

The radial vibration of isotropic thin elastic circular rings is studied and the equivalent circuit is obtained. Based on the equivalent circuit, the resonance frequency equation is derived and the resonance frequency is obtained. By means of the numerical methods, the root of the resonance frequency equation is solved, and the relation between the roots and the Poisson's ratio is fitted. The relationship between the vibrational mode and the geometrical dimensions of the ring is analyzed. The conclusions are beneficial to the design and calculation of the radial vibration of the thin circular ring used in ultrasonic technologies.