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

Sara Canning, Alan Walker, Paul Roach

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Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. 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 sensor 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 surpasses traditional design sensors.
Original languageEnglish
Article number2170
Number of pages16
Issue number12
Early online date17 Dec 2016
Publication statusE-pub ahead of print - 17 Dec 2016


  • piezoelectric materials
  • mathematical modelling
  • Sierpinski tetrix fractal
  • ultrasonic transducer
  • renormalization
  • finite differences


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