Renormalisation analysis of a composite ultrasonic transducer with a fractal architecture

Ebrahem Algehyne, Anthony J. Mulholland

Research output: Contribution to journalArticle

1 Citation (Scopus)
63 Downloads (Pure)

Abstract

To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behaviour by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this article we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modelled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretised equations yields to a renormalisation methodology which is used to derive expressions for the non-dimensionalised electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.
Original languageEnglish
Article number1750015
Number of pages14
JournalFractals
Volume25
Issue number2
DOIs
Publication statusPublished - 12 Apr 2017

Fingerprint

Ultrasonic transducers
Transducer
Renormalization
Fractals
Fractal
Composite
Length Scale
Composite materials
Aircraft plants
Transducers
Range of data
Acoustic impedance
Piezoelectric transducers
Ultrasound
Graph in graph theory
Impedance
Aircraft
Polymers
Pipelines
Safety

Keywords

  • piezoelectric
  • polymer
  • finite element method
  • fractal
  • ultrasound
  • transducer
  • renormalisation

Cite this

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Renormalisation analysis of a composite ultrasonic transducer with a fractal architecture. / Algehyne, Ebrahem; Mulholland, Anthony J.

In: Fractals, Vol. 25, No. 2, 1750015, 12.04.2017.

Research output: Contribution to journalArticle

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