An improved lumped parameter model of the single free-flooded ring transducer using Helmholtz–Kirchhoff integral solution

The Helmholtz-Kirchhoff integral (HKI) may be considered as the boundary element method (BEM) used to calculate the acoustic pressure at any position in the 3D-radiation problem from a vibrating surface. This method provides valuable insights into the radiation characteristics of vibrating structures, which may offer significant information and tools to underwater transducer design engineers during the early stages of development. It may save considerable computational costs in the design processes for the underwater transducer such as Hull Mount Sonar. This study illustrates usefulness of the HKI-based approach by developing a simple model of the Free Flooded Ring (FFR) transducer using a piezoelectric ring model and the HKI solution on the surface acoustic pressure of the ring through their physical conditions on their connected interfaces. The FFR transducer is widely utilized as a low-frequency acoustic source in underwater environments due to its broad operating frequency bandwidth and relatively small size. The developed approach aims to construct a precise model that considers the sound-structure interactions between the piezoelectric ring and the acoustic medium around it. To validate the accuracy of the proposed method, the acoustic pressure and electrical admittance are compared with those obtained through finite element method (FEM) simulations.