Transducer arrays are commonly analyzed by the finite element method (FEM) with high accuracy, but it is costly, particularly when having flexible surrounding structures. In this study, we developed an equivalent circuit (EC)-based model of an array of transducers with flexible surrounding structures for effective analysis. The impedance matrix was first constructed by coupling the electrical, mechanical impedance, and the acoustic radiation impedance obtained by the EC method and finite element-boundary element (FE-BE) coupling method. The transfer matrix of far-field pressure to the transducer response was then constructed by the FE-BE coupling method, and finally the sound pressure of the external acoustic field was obtained. To verify the accuracy, the results of the proposed method were compared with those of the conventional FEM. To evaluate the efficiency of the proposed method, the reduction in the degrees of freedom (DOFs) of the proposed method from the conventional FEM analysis was investigated. The simulation results of the proposed method are highly accurate and efficient. The proposed method is expected to be useful for conceptual design.

We developed and experimentally realized a novel type of focal transducer called a void-centric zone plate ultrasonic transducer (VZPUT). Although VZPUT is a planar transducer, it can focus ultrasound and control the focal length using a single-channel electric network. Further, unlike a classical Fresnel zone plate, the VZPUT has space for an imaging probe at the center, making it useful for therapeutic focused ultrasound (FUS). To realize VZPUT, we develop a novel void-centric zone plate (VZP) that allows design freedom for the radius of the space at the center. Then, we fabricate the piezoelectric VZP, an acoustic metamaterial, considering its structural vibration modes that appear within the operating frequency range. The VZPUT demonstrated applicability to therapeutic FUS in that it could control the focal point by the operating frequency with real-time monitoring images from the imaging probe mounted at the center.

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