A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Currently manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the
implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first transducer design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously
investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device, at its fifth fractal generation level, achieves a RFR bandwidth greater than that of the Sierpinski gasket-inspired transducer and a significant increase in the amplitude and gain bandwidth product compared to a tradition design.