A Finite Element Approach to Modelling Fractal Ultrasonic Transducers

Ebrahem Algehyne, Anthony Mulholland

Research output: Other contribution

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 bandwith 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.
LanguageEnglish
TypeResearch Report
PublisherUniversity of Strathclyde
Number of pages60
Place of PublicationGlasgow
Publication statusUnpublished - 2014

Publication series

Name
No.1

Fingerprint

Transducer
Fractal
Finite Element
Length Scale
Modeling
Sierpinski Gasket
Ultrasonic Wave
Composite Structures
Ultrasound
Resonator
Performance Measures
Impedance
Euclidean
Composite
Mathematical Model
Propagation
Predict
Range of data
Design

Keywords

  • fractal ultrasonic transducers
  • modelling
  • finite element method

Cite this

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A Finite Element Approach to Modelling Fractal Ultrasonic Transducers. / Algehyne, Ebrahem; Mulholland, Anthony.

60 p. Glasgow : University of Strathclyde. 2014, Research Report.

Research output: Other contribution

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T1 - A Finite Element Approach to Modelling Fractal Ultrasonic Transducers

AU - Algehyne, Ebrahem

AU - Mulholland, Anthony

PY - 2014

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N2 - 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 bandwith 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.

AB - 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 bandwith 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.

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KW - finite element method

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