Electromechanical equivalent circuit and coupled vibration of the radially composite cylindrical piezoelectric transducer

Abstract

Electromechanical equivalent circuit for the radially composite cylindrical piezoelectric transducer in coupled vibration is deduced. The transducer is composed of a piezoelectric cylinder sandwiched by two concentric metal cylinders. Equivalent elasticity method is used to study the coupled vibrations of the three cylinders. A ratio named the mechanical coupling coefficient is introduced to divide the coupled vibration into the radial and longitudinal vibrations. The electromechanical equivalent circuits for the transducer and the resonance frequency equations are obtained. When the height is close to the radius of the transducer, the coupling between the radial vibration and the longitudinal vibration is strong. The thicker is the piezoelectric cylinder, the larger is the effective electromechanical coupling coefficient. Several prototypes of the transducer are fabricated. It is demonstrated that the theoretical resonance frequencies are in good agreement with the numerical and experimental results.