### Abstract

Original language | English |
---|---|

Media of output | Research Report |

Publisher | University of Strathclyde |

Number of pages | 119 |

Publication status | Unpublished - 2015 |

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### Keywords

- ultrasound
- finite element method
- fractal
- renormalisation

### Cite this

*University of Strathclyde*.

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*A Composite Ultrasonic Transducer with a Fractal Architecture*. University of Strathclyde.

**A Composite Ultrasonic Transducer with a Fractal Architecture.** / Algehyne, Ebrahem A.; Mulholland, Anthony J.

Research output: Other contribution

TY - GEN

T1 - A Composite Ultrasonic Transducer with a Fractal Architecture

AU - Algehyne, Ebrahem A.

AU - Mulholland, Anthony J.

PY - 2015

Y1 - 2015

N2 - 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 its resonant behaviour by the use of a single length scale in its 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 homogenised (standard) design shows some benefits of these fractal designs.

AB - 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 its resonant behaviour by the use of a single length scale in its 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 homogenised (standard) design shows some benefits of these fractal designs.

KW - ultrasound

KW - finite element method

KW - fractal

KW - renormalisation

M3 - Other contribution

PB - University of Strathclyde

ER -