Analysis and Optimization of Bending Vibration Modes of a Trilaminar Bending Ring Transducer with Unequal Diameters

In this study, we propose a fast calculation method that utilizes Kirchhoff’s hypotheses and electroelasticity theory to derive the resonant frequency, antiresonant frequency, and effective electromechanical coupling coefficient of a trilaminar bending ring transducer with unequal diameters. The accuracy of the theoretical method is validated through finite element analysis (FEM) and experimental tests. Furthermore, we perform optimization of the effective electromechanical coupling coefficient of the first-order bending vibration of the trilaminar bending ring transducer. Our optimization results indicate that, under the free inner and fixed outer boundary conditions, the effective electromechanical coupling coefficient initially increases to a maximum value and then rapidly decreases as r1/r2 increases. This behavior can be attributed to the out-of-phase vibrations and the in-phase electric field excitation on both sides of the bending ring vibration nodal circle. Finally, we present the optimized size configuration required to achieve the maximum effective electromechanical coupling coefficient. This study provides theoretical guidance for the design and optimization of trilaminar bending ring transducers with unequal diameters and has the potential to significantly advance the field of crosswell seismic source technology.