Abstract: The radial vibration of an annular ultrasonic concentrator with nth power thickness variation was studied. Based on the electromechanical analogy, the radial equivalent circuit and the frequency equation were derived. The displacement amplitude magnification coefficient of the concentrator was obtained. The relationships between the resonance frequency, the radial displacement amplitude magnification coefficient of the concentrator at the first and second order vibration modal and the radius ratio of it were analyzed. By numerical calculation, it is shown that the radial fundamental frequency of the concentrator decreases as the radius ratio increases. While a minimum of the second order resonance frequency appears when the radius ratio of the annular concentrator increases. Moreover, the displacement amplitude magnification coefficient of the concentrator increases as the power of nth increases, and the amplitude magnification coefficient at the second order resonance is much greater than that of the first order resonance. It is illustrated that the theoretical results are in good agreement with the FEM simulations.

Key words: annular concentrator, amplitude magnification coefficient, equivalent circuit, frequency equation