A finite element approach to modelling fractal ultrasonic transducers

Algehyne, Ebrahem A. and Mulholland, Anthony J. (2015) A finite element approach to modelling fractal ultrasonic transducers. IMA Journal of Applied Mathematics, 80 (6). pp. 1684-1702. ISSN 1464-3634 (https://doi.org/10.1093/imamat/hxv012)

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Abstract

Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwidth device it would seem natural therefore to utilize resonators that span a range of length scales. In this article we derive a mathematical model to predict the dynamics of a fractal ultrasound transducer; the fractal in this case being the Sierpinski gasket. Expressions for the electrical and mechanical fields that are contained within this structure are expressed in terms of a finite element basis. The propagation of an ultrasonic wave in this transducer is then analyzed and used to derive expressions for the non-dimensionalised electrical impedance and the transmission and reception sensitivities as a function of the driving frequency. Comparing these key performance measures to an equivalent standard (Euclidean) design shows some benefits of these fractal designs.

ORCID iDs

Algehyne, Ebrahem A. and Mulholland, Anthony J. ORCID logoORCID: https://orcid.org/0000-0002-3626-4556;
  • Item type:Article
    ID code:52871
    Dates:
    Date
    Event
    1 December 2015
    Published
    29 May 2015
    Published Online
    21 April 2015
    Accepted
    Notes:This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Algehyne, E. A., & Mulholland, A. J. (2015). A finite element approach to modelling fractal ultrasonic transducers. IMA Journal of Applied Mathematics, 80(6), 1684-1702. is available online at: http://imamat.oxfordjournals.org/content/80/6/1684.abstract
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:06 May 2015 08:34
    Last modified:11 Nov 2024 11:04
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/52871
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