Linear ultrasonic array incorporating a Cantor Set fractal element configuration

The resonance frequency of an active element in a piezoelectric ultrasonic transducer is dependent on its length scale. Inspired by natural occurring auditory systems, incorporation of elements with varying length scales in the piezoelectric transducer design can result in a wider operational bandwidth. In this paper, a mathematical algorithm was developed first to define the feature of a fractal geometry called the Cantor Set (CS), then a series of parameter sweep simulations are performed to design a CS fractal array transducer and a conventional array transducer and optimize their performance. The behaviors of these two array transducers were explored theoretically, using finite element modeling and experimentally using the scanning laser vibrometry. The FE simulation results and experimental results correlate well with each other, which indicates an approximate 30% operating bandwidth enhancement and a 5 dB side lobe reduction can be achieved by the CS fractal array compared to the conventional linear array design.