Free-flooded ring (FFR) transducers are widely used low-frequency underwater transducers with broad bandwidth and compact size. This paper presents two modified lumped-parameter models (mLPMs) and a hybrid model for analyzing the electrical and acoustic properties of an FFR transducer. A radiation impedance matrix calculated using the Kirchhoff–Helmholtz integral was employed to account for acoustic loading effects. The resonance frequencies in cavity and ring modes predicted by the mLPMs showed good agreement with finite element simulations, with relative errors within 1%. The hybrid model further captured bending-mode resonance and beam patterns by considering non-uniform radial velocities. Acoustic beam patterns demonstrated that the mLPMs describe the axial side lobe in cavity mode, while the hybrid model provides more accurate predictions across all modes. These findings indicate that the mLPMs serve as efficient tools for predicting the operational band between cavity and ring modes, whereas the hybrid model is required for scenarios involving bending vibrations. Beyond single-element analysis, the proposed models may serve as a foundation for future control-oriented array applications in sonar systems.
Lee et al. (Fri,) studied this question.