Investigating the Performance of a Fractal Ultrasonic Transducer Under Varying System Conditions

Barlow, Euan; Algehyne, Ebrahem A.; Mulholland, Anthony J.

doi:10.3390/sym8060043

Cited by 4 publications

(4 citation statements)

References 33 publications

(65 reference statements)

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“…Sensor performance optimization could also be employed with the aim of improving the values of the RFR bandwidth, amplitude and gain bandwidth product. This could be achieved by sampling different material parameters, such as piezoelectric constant and Young’s modulus [34]. This provides an opportunity to ascertain a range of materials that could be used in the creation of novel fractal-inspired ultrasonic sensors.…”

Section: Discussionmentioning

confidence: 99%

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

Walker

Roach

2016

Sensors

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Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first sensor design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device surpasses traditional design sensors.

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Section: Discussionmentioning

confidence: 99%

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

Walker

Roach

2016

Sensors

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“…The former case is modeled using a renormalization approach whereas the latter case is modeled using homogenization (simple). In a previously published paper, 31,43 only ceramic elements were used, however in this paper, this was improved on by using a combination of ceramic and polymer elements. New basis functions, whose support is the underlying fractal graph, were developed for the finite element analysis.…”

Section: Discussionmentioning

confidence: 99%

Renormalization Analysis of a Composite Ultrasonic Transducer With a Fractal Architecture

Algehyne¹,

Mulholland²

2017

Fractals

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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 behavior 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 paper, 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 modeled 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 discretized equations yields to a * Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 1750015-1 E. A. Algehyne & A. J. Mulhollandrenormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

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“…Another area of interest would be in transducer performance optimization akin to that done for the Sierpinski gasket pre-fractal. 33 A technique for increasing the values for each of the figures of merit could be achieved by sampling different material parameters. This may assist in establishing the optimal material that could be used for ultrasonic transducers.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Figure 6 shows the comparison for the electrical impedance between the three Sierpinski carpet models (Ẑ E,η ,Ẑ E,δ ,Ẑ E,γ ), the Sierpinski gasket (Ẑ E,G ) and Euclidean (Ẑ E,E ) transducers. Electrical impedance profiles are important Piezoelectric stress e 33 as they allow us to determine the potential efficiency of the theoretical transducer. The features of interest from these plots are the occurrence of the electrical and mechanical resonant frequencies.…”

Section: Comparison and Effectiveness Of Standard And Pre-fractal Tramentioning

confidence: 99%

The Effectiveness of a Sierpinski Carpet-Inspired Transducer

Walker

Roach

2017

Fractals

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Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Standard designs have a regular structure and therefore operate effectively over narrow bandwidths due to their single length scale. Naturally occurring transducers benefit from a wide range of length scales giving rise to increased bandwidths. It is therefore of interest to investigate structures which incorporate a range of length scales, such as fractals. This paper applies an adaptation of the Green function renormalization method to analyze the propagation of an ultrasonic wave in a series of pre-fractal structures. The structure being investigated here is the Sierpinski carpet. Novel expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the operating frequency are presented. Comparisons of metrics between three new designs alongside the standard design (Euclidean structure) and the previously investigated Sierpinski gasket device are performed. § Corresponding author. The results indicate a significant improvement in the reception sensitivity of the device, and improved bandwidth in both the receiving and transmitting responses. 1750050-1

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Investigating the Performance of a Fractal Ultrasonic Transducer Under Varying System Conditions

Cited by 4 publications

References 33 publications

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

Renormalization Analysis of a Composite Ultrasonic Transducer With a Fractal Architecture

The Effectiveness of a Sierpinski Carpet-Inspired Transducer

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