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.

In order to improve the detection range and imaging resolution of dipole remote detection logging, an optimal nonlinear frequency modulation (ONLFM) excitation method is proposed in this paper. In this method, the optimal waveform model of the sound source is designed with objective functions of SNR and resolution to obtain the highest resolution under the condition of the required SNR. This optimal model is a multi-constraint optimization problem, and the simulated annealing method has been used to solve it. Solving the optimal model can obtain the optimal spectrum, and the ONLFM waveform can be designed by using the stationary phase principle. Compared with the electric pulse sound source used in traditional technology, this ONLFM sound source can improve the energy and extend the frequency band range of the reflected wave, which can provide the higher resolution and SNR. The simulation results show that the ONLFM sound source can effectively improve the SNR and resolution of the reflected wave, and the detection range and imaging resolution of dipole shear wave remote detection will be improved.

Key detection performance metrics, particularly resolution, are largely determined by the design parameters of ultrasonic arrays. The structural design of the transducer strongly influences critical indicators, including side lobe levels, beam directivity, and focal spot size. To improve parameter selection, this study proposes a multi-objective optimization strategy specifically tailored for cylindrical surface ultrasonic transducers. The geometric parameters of the array and the variables influencing resolution performance are mapped in a nonlinear manner. The NSGA-II algorithm is employed to perform extremum seeking optimization on a trained BPNN, generating a Pareto-optimal solution set by specifying main-lobe width, side-lobe intensity, and sound-pressure uniformity as optimization objectives. For validation, the geometric configurations derived from this solution set are applied in acoustic field simulations. Simulation results demonstrate that the dynamic aperture exhibits clear regularity when the array settings meet millimeter-level resolution requirements. These findings support real-world engineering applications and provide valuable insights for enhancing the geometric design of cylindrical ultrasonic arrays.