Study on the Longitudinal–Radial Coupled Vibration of Cascade Cylindrical Piezoelectric Transducers

Abstract

Abstract. Cascade cylindrical piezoelectric transducers (CCPTs) are widely used in ultrasonic engineering, and accurate vibration analysis is essential for understanding their operating mechanisms. Traditional one-dimensional (1D) vibration theory assumes the transducer's length significantly exceeds its diameter, neglecting radial vibrations. However, in practical applications, radial dimensions influence the overall vibration behavior and must be considered. In this article, the equivalent elastic method is applied to analyze the coupled longitudinal–radial vibration of CCPTs by introducing a mechanical coupling coefficient. An electromechanical equivalent circuit is formulated, from which resonance frequency equations and the effective electromechanical coupling coefficient are derived. Numerical and experimental results demonstrate that the method agrees well with finite element method results and predicts the vibration behavior more accurately than the 1D theory. In addition, the equivalent elastic method reveals the influence of geometric dimensions and material parameters on the coupled vibration behavior. The results indicate that when the longitudinal and radial dimensions approach each other, the mechanical coupling becomes strong and the radial vibration must be considered in vibration analysis.