Theoretical modeling and numerical simulation evaluation of medical broadband ellipsoidal transducers

Purpose This study aims to address the critical research gap in modeling and analyzing axisymmetric piezoelectric ellipsoidal shells. Its purpose is to overcome the limitations of existing simplified axisymmetric models by developing a comprehensive theoretical framework that accurately characterizes complex electromechanical coupling and vibration modes. Design/methodology/approach A rigorous analytical model is established using 3-D piezoelectric theory and thin-shell dynamics. Governing equations account for curvature variation in both meridional and azimuthal directions. A generalized electromechanical equivalent circuit (EEC) model is then derived to capture curvature coupling and anisotropic modes. Findings Resonant frequencies depend strongly on aspect ratio (a/b) and thickness; the model predicts values within 0.33% of finite-element results. The generalized EEC quantifies geometry-induced anisotropy and modal coupling. Broadband transmitting voltage response (TVR) rises monotonically from 10 dB (200 kHz) to 46 dB (1,400 kHz), yielding 1,200 kHz bandwidth. Directional analysis shows stable bilobate beams (DI ≈14.2 dB) maintained across 200–1,400 kHz, outperforming spherical and thin-disk counterparts. Research limitations/implications This study presents a theoretical framework and numerical validation. The main limitation is the lack of experimental measurements to confirm the simulated performance. Future work must focus on prototype fabrication, experimental TVR and directivity index characterization in water tanks and safety evaluation for specific applications such as medical ablation. Practical implications This elliptical three-layer architecture enables the development of miniaturized, high-performance ultrasonic devices without compromising bandwidth or directivity. It proposes a novel approach to addressing the critical size–performance trade-off challenges inherent in medical ultrasound imaging, wearable energy harvesting and underwater detection applications, achieving system dimension reduction and assembly complexity minimization concomitant with performance enhancement. The established simulation framework provides a robust foundation for rapid commercialization, offering a cost-effective upgrade pathway for existing piezoelectric transducer product lines with substantial market potential. Social implications By enabling smaller, higher performance ultrasonic devices, this work advances accessibility to compact medical ultrasound imaging for point-of-care and rural diagnostics, reducing reliance on large, expensive equipment. It also supports the development of efficient wearable energy harvesters for self-powered electronics, lowering long-term energy consumption and electronic waste. These improvements ultimately contribute to more equitable health-care access and more sustainable wearable technology development. Originality/value This work presents the first, to the best of the authors’ knowledge, comprehensive framework and generalized EEC for axisymmetric ellipsoidal transducers. It combines differential geometry with separation-of-variables to derive closed-form resonance/anti-resonance expressions and design rules. The findings, derived from a comprehensive theoretical and numerical study, indicate the potential for a new design strategy toward miniaturized, broadband, high-directivity devices for medical ultrasound and wearable energy harvesting, indicating the classic miniaturization-directivity trade-off.