ANALYSIS OF ULTRASONIC TRANSDUCERS WITH FRACTAL ARCHITECTURE
Abstract
Ultrasonic transducers composed of a periodic piezoelectric composite are generally accepted as the design of choice in many applications. Their architecture is normally very regular and this is due to manufacturing constraints rather than performance optimization. Many of these manufacturing restrictions no longer hold due to new production methods such as computer controlled, laser cutting, and so there is now freedom to investigate new types of geometry. In this paper, the plane wave expansion model is utilized to investigate the behavior of a transducer with a self-similar architecture. The Cantor set is utilized to design a 2-2 configuration, and a 1-3 configuration is investigated with a Sierpinski carpet geometry. Ideally a single longitudinal mode in the thickness direction will drive the transducer in a piston-like fashion. In this paper it was found that by increasing the fractal generation level, the bandwidth surrounding the main thickness mode will increase, but there will be a corresponding reduction in the amplitude of the electrical conductance. It is also shown that a shift in the frequency of operation of the device can be achieved by altering the spatial periodicity of the electrical excitation.
