Electro-mechanical equivalent circuit of a piezoelectric ceramic thin circular ring in radial vibration

The radial vibration of a piezoelectric ceramic thin circular ring polarized in the thickness direction is studied. Its electro-mechanical equivalent circuit is derived, the resonance and anti-resonance frequency equations are obtained, and the relationship between the resonance frequencies and the material parameters and the geometrical dimensions is analyzed. It is illustrated that the first radial resonance frequency of a solid piezoelectric thin plate is larger than that of a hollow piezoelectric thin ring with the same outer radius. When the radius ratio is increased, the first radial resonance frequency is decreased. The relationship between the second radial resonance frequency and the radius ratio is complex. When the radius ratio is smaller than the definite value, the second radial resonance frequency is decreased as the radius ratio is increased; while when the radius ratio is larger than this value, the second radial resonance frequency is increased as the radius ratio is increased. When the radius ratio is larger than a definite value, the second radial resonance frequency is larger than that of a solid plate with the same outer radius. When the radius ratio limits one, the second radial resonance frequency limits infinity.