Analysis of the transmitting characteristics of an acoustic conformal array of multimode tonpilz transducers by the equivalent circuit method

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Commonly used underwater acoustic array types include planar and conformal arrays. The conformal array is favorable in practical active sonar systems as it offers superior acoustic performance, but its relatively complicated structure requires sophisticated analysis and design. In general, the characteristics of the array are analyzed using the finite element method (FEM). However, for complicated structures like the conformal array, the FEM is extremely time consuming and computation intensive. In this work, we developed a new equivalent circuit method (ECM) that can facilitate the analysis of the acoustical performance of a conformal array. The proposed ECM can include the effect of mutual interference between constitutive elements of the conformal array in addition to its own property of the array, which has not been possible with conventional equivalent circuits. The new ECM was applied to the analysis of the transmitting characteristics of a conformal array of multimode Tonpilz transducers. The Tonpilz transducer operated at both longitudinal- and flexural-mode resonances simultaneously to achieve a wide bandwidth. A new equivalent circuit to represent the multimodal properties of the Tonpilz transducer itself was derived as well. The validity and efficiency of the analysis of the Tonpilz transducer and the conformal array was verified by comparing the transmitting voltage response spectrum obtained by the ECM with those obtained by the FEM and experimental measurement. For the experimental validation, prototypes of the multimode Tonpilz transducers and their conformal array were fabricated and characterized.