title: A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer.
abstract: 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.
authors.affiliation: School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, UK. sara.koubayssi@southwales.ac.uk.
authors.forename: Sara
authors.initials: S
authors.lastname: Canning
authors.affiliation: School of Science and Sport, University of the West of Scotland, Paisley PA1 2BE, UK. alan.walker@uws.ac.uk.
authors.forename: Alan J
authors.initials: AJ
authors.lastname: Walker
authors.affiliation: School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, UK. paul.roach@southwales.ac.uk.
authors.forename: Paul A
authors.initials: PA
authors.lastname: Roach
keywords: Sierpinski tetrix fractal; finite differences; mathematical modelling; piezoelectric materials; renormalization; ultrasonic transducer