Radial vibration of step-type radial transformers

Radial vibration of a thin circular metallic ring is studied.The equivalent circuit is derived.Based on the equivalent circuit,the step-type radial transformer consisting of two such rings is analyzed.The composite equivalent circuit is derived and the resonance frequency equation obtained.Relationship among the resonance frequency,the radial displacement amplitude magnification and the geometrical dimensions is analyzed.The resonance frequency of the step-type radial transformer is obtained with an analytical meth-od as well as a numerical method.The two results are in good agreement.