Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots

The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.