The equivalent circuit of the annular plate concentrator with power function cross-section in radial vibration

Based on the principle of electro-mechanical analogy and the plane stress equation of a thin annular plate with thickness variation,the equivalent circuit,the resonance frequency equation and the displacement amplitude magnification coefficient of the annular plate concentrator with power function cross-section in radial vibration are derived.The relationships between the radius ratio and the radial resonance frequency and the displacement amplitude magnification coefficient at the first and second order resonance modes of the concentrator are analyzed.The result shows that the equivalent circuit of the annular plate concentrator with power function cross-section in radial vibration is a novel non-reciprocal two-port equivalent network.The first and second resonance frequencies of the concentrator increase as its radius ratio increases;the displacement amplitude magnification coefficient decreases firstly and then increases as the radius ratio increases at the first order radial resonance mode;the displacement amplitude magnification coefficient increases as the radius ratio increases at the second order radial resonance mode.The displacement amplification magnification coefficient at the second order resonance mode is larger than that of the first order resonance mode,so the second order radial resonance mode has better radial vibration performance.The theory results are confirmed by the finite element method(COMSOL Multiphysics).According to the equivalent circuit model of the annular plate concentrator with power function cross-section,a piezoelectric ceramic annular transducer is designed;the first and second order radial resonance,anti-resonance frequency and the effective electro-mechanical coupling coefficient of the piezoelectric transducer are calculated.The results are in good agreement with the finite element method.It provides a concise design theory for the engineering application of the annular plate concentrator with power function cross-section and the related piezoelectric transducer.It is expected to be used as a radial ultrasonic cutting knife used in ultrasonic engineering.