Abstract
This study proposes the theoretical optimal patterning method based on the geometrical transformation acoustics to design an ultrasonic omnidirectional transducer system, which is composed of the designed near zero-index acoustic metamaterial (ZIAMM). The designed ZIAMM is made of circular rubber rods in water matrix. Meanwhile, the curved unit cell structure is necessary to arrange the designed ZIAMM effectively into the circular-shaped ultrasonic omnidirectional transducer system. To this end, we transform the square unit cell into the curved unit cell in the physical space, instead of starting from a homogeneous medium. Also the periodic boundary condition in the two-dimensional polar coordinate is proposed to calculate the dynamic characteristic (i.e., the effective material properties and the dispersion relation) according to the curvature of curved unit cell. The proposed optimal patterning method is verified through the ZIAMM-based ultrasonic omnidirectional transducer system. Especially the radiation performance of ZIAMM-based ultrasonic omnidirectional transducer system is greatly improved by this optimal patterning.
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