Renormalisation analysis of a composite ultrasonic transducer with a fractal architecture

Ebrahem Algehyne, Anthony J. Mulholland

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
67 Downloads (Pure)


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
Issue number2
Publication statusPublished - 12 Apr 2017


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


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