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

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

Investigating the performance of a fractal ultrasonic transducer under varying system conditions

As applications become more widespread there is an ever-increasing need to improve the accuracy of ultrasound transducers, in order to detect at much finer resolutions. In comparison with naturally occurring ultrasound systems the man-made systems have much poorer accuracy, and the scope for improvement has somewhat plateaued as existing transducer designs have been iteratively improved over many years. The desire to bridge the gap between the man-made and naturally occurring systems has led to recent investigation of transducers with a more complex geometry, in order to replicate the complex structure of the natural systems. These transducers have structures representing fractal geometries, and these have been shown to be capable of delivering improved performance in comparison with standard transducer designs. This paper undertakes a detailed investigation of the comparative performance of a standard transducer design, and a transducer based on a fractal geometry. By considering how these performances vary with respect to the key system parameters, a robust assessment of the fractal transducer performance is provided

Additive manufacturing (3D print) of air-coupled diaphragm ultrasonic transdrucers

Air-coupled ultrasound is a non-contact technology that has become increasingly common in Non Destructive Evaluation (NDE) and material evaluation. Normally, the bandwidth of a conventional transducer can be enhanced, but with a cost to its sensitivity. However, low sensitivity is very disadvantageous in air-coupled devices. This thesis proposes a methodology for improving the bandwidth of an air-coupled micro-machined ultrasonic transducer (MUT) without sensitivity loss by connecting a number of resonating pipes of various length to a cavity in the backplate. This design is inspired by the pipe organ musical instrument, where the resonant frequency (pitch) of each pipe is mainly determined by its length. The −6 dB bandwidth of the "pipe organ" inspired air-coupled transducer is 55.7% and 58.5% in transmitting and receiving modes, respectively, which is ∼5 times wider than a custom-built standard device. After validating the concept via a series of single element low-frequency prototypes, two improved designs: the multiple element and the high-frequency single element pipe organ transducers were simulated in order to tailor the pipe organ design to NDE applications.Although the simulated and experimental performance of the pipe organ inspired transducers are proved to be significantly better than the conventional designs, conventional micro-machined technologies are not able to satisfy their required 3D manufacturing resolution. In recent years, there has been increasing interest in using additive manufacturing (3D printing) technology to fabricate sensors and actuators due to rapid prototyping, low-cost manufacturing processes, customized features and the ability to create complex 3D geometries at micrometre scale. This work combines the ultrasonic diaphragm transducer design with a novel stereolithographic additive manufacturing technique. This includes developing a multi-material fabrication process using a commercial digital light processing printer and optimizing the formula of custom-built functional (conductive and piezoelectric) materials. A set of capacitive acoustic and ultrasonic transducers was fabricated using the additive manufacturing technology. The additive manufactured capacitive transducers have a receiving sensitivity of up to 0.4 mV/Pa at their resonant frequency.Air-coupled ultrasound is a non-contact technology that has become increasingly common in Non Destructive Evaluation (NDE) and material evaluation. Normally, the bandwidth of a conventional transducer can be enhanced, but with a cost to its sensitivity. However, low sensitivity is very disadvantageous in air-coupled devices. This thesis proposes a methodology for improving the bandwidth of an air-coupled micro-machined ultrasonic transducer (MUT) without sensitivity loss by connecting a number of resonating pipes of various length to a cavity in the backplate. This design is inspired by the pipe organ musical instrument, where the resonant frequency (pitch) of each pipe is mainly determined by its length. The −6 dB bandwidth of the "pipe organ" inspired air-coupled transducer is 55.7% and 58.5% in transmitting and receiving modes, respectively, which is ∼5 times wider than a custom-built standard device. After validating the concept via a series of single element low-frequency prototypes, two improved designs: the multiple element and the high-frequency single element pipe organ transducers were simulated in order to tailor the pipe organ design to NDE applications.Although the simulated and experimental performance of the pipe organ inspired transducers are proved to be significantly better than the conventional designs, conventional micro-machined technologies are not able to satisfy their required 3D manufacturing resolution. In recent years, there has been increasing interest in using additive manufacturing (3D printing) technology to fabricate sensors and actuators due to rapid prototyping, low-cost manufacturing processes, customized features and the ability to create complex 3D geometries at micrometre scale. This work combines the ultrasonic diaphragm transducer design with a novel stereolithographic additive manufacturing technique. This includes developing a multi-material fabrication process using a commercial digital light processing printer and optimizing the formula of custom-built functional (conductive and piezoelectric) materials. A set of capacitive acoustic and ultrasonic transducers was fabricated using the additive manufacturing technology. The additive manufactured capacitive transducers have a receiving sensitivity of up to 0.4 mV/Pa at their resonant frequency

Broadband 1-3 piezoelectric composite transducer design using Sierpinski Gasket fractal geometry

Wider operational bandwidth is an important requirement of an ultrasound transducer across many applications. In nature, it can be observed that several hearing organs possess a broad operating bandwidth by having a varying length scales structure. Moreover, conventional 1-3 piezoelectric composite transducers have been widely recognized for their wider bandwidth over their piezoelectric ceramic counterparts. In this paper, a novel 1-3 piezoelectric composite design using a fractal geometry, known as the Sierpinski Gasket (SG), is proposed in order to explore the potential of further extending the operational bandwidth and sensitivity of the transducer. Two equivalent 1-3 piezocomposite designs are compared to this end, one with a conventional periodic parallelepiped shaped pillar structure and one with the SG fractal geometry, both theoretically, using a finite element (FE) analysis package, and experimentally. The transmit voltage response and open circuit voltage response are used to illustrate bandwidth improvement from the fractal composite design. Following the simulation results, a 580 kHz single element transducer, utilizing the proposed SG fractal microstructure, is fabricated using a pillar placement methodology. The performance of the prototyped device is characterized and compared with a conventional 1-3 composite design, as well as with a commercial ultrasound transducer. In the one-way transmission mode, a bandwidth improvement of 27.2 % and sensitivity enhancement of 3.8 dB can be found with the SG fractal design compared to an equivalent conventional composite design and up 105.1 % bandwidth improvement when compared to the commercial transducer. In the one-way reception mode, the bandwidth improvement for the SG fractal design is 2.5 % and 32.9 % when compared to the conventional and commercial transducers, respectively

Analysis of a fractal ultrasonic transducer with a range of piezoelectric length scales

The transmission and reception sensitivities of most piezoelectric ultrasonic transducers are enhanced by their geometrical structures. This structure is normally a regular, periodic one with one principal length scale which, due to the resonant nature of the devices, determines the central operating frequency. There is engineering interest in building wide bandwidth devices, and so it follows that in their design, resonators that have a range of length scales should be used. This paper describes a mathematical model of a fractal ultrasound transducer whose piezoelectric components span a range of length scales. There have been many previous studies of wave propagation in the Sierpinski gasket but this paper is the first to study its complement. This is a critically important mathematical development as the complement is formed from a broad distribution of triangle sizes whereas the Sierpinski gasket is formed from triangles of equal size. Within this structure, the electrical and mechanical fields fluctuate in tune with the time dependent displacement of these substructures. A new set of basis functions is developed that allow us to express this displacement as part of a finite element methodology. A renormalisation approach is then used to develop a recursion scheme that analytically describes the key components from the discrete matrices that arise. Expressions for the transducer's operational characteristics are then derived and analysed as a function of the driving frequency. It transpires that the fractal device has a significantly higher reception sensitivity (18 dB) and a significantly wider bandwidth (3 MHz) than an equivalent Euclidean (standard) device

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Design, modelling, characterization and implementation of acoustic lenses for modulation of ultrasound beams.

Tesis por compendio[ES] La capacidad de controlar y modificar los haces de energía ha sido motivo de investigación por parte de la comunidad científica desde largo tiempo atrás. En el campo de la acústica, este control energético de las ondas mecánicas tiene numerosas aplicaciones. Desde las aplicaciones industriales, alimentarias, farmacéuticas, etcétera hasta la biomedicina. Esta tesis se basa en la aplicación del control y modulación focal de los ultrasonidos para el uso en este último campo. Se puede modular y controlar los focos de ultrasonidos de diferentes formas. En este caso, se han desarrollado lentes planas que utilizan el principio de la difracción para lograr focalizar los haces. Las ventajas del uso de lentes planas de focalización permiten ser implementadas de forma sencilla en procesos de mecanización e incluso mediante impresión 3D. Se propone utilizar transductores planos que al emitir sobre una lente acústica, se produzca una conformación focal de características controladas. La lente conocida como lente de Fresnel (FZP) ha sido escogida como base de diseño en la implementación de las diferentes soluciones que logran cumplir con los objetivos marcados. Mediante la aplicación de modificaciones en una FZP se puede lograr pasar de una lente con capacidades extraordinarias de focalización a una lente capaz de controlar la resolución lateral y la profundidad de foco e incluso mejorar la ganancia. El objetivo final de aplicación es el uso en transductores de ultrasonidos de alta intensidad conocidos como HIFU. Mejorar la capacidad de resolución hace que se puedan desarrollar mejores terapias oncológicas que supongan un índice mayor de éxito en la lucha contra el cáncer. En la presente tesis se ha propuesto, además, una novedosa lente FZP basada en el cambio de fase que puede resultar un antes y un después en aplicaciones biomédicas. Se ha conseguido no solo mejorar la eficiencia de una FZP, sino que se ha conseguido implementar en materiales compatibles con resonancia magnética. Se han desarrollado modelos numéricos basados en el método de los elementos finitos que emulan la física involucrada. Las medidas han sido realizadas en condiciones controladas por un sistema robotizado de alta precisión. Todos los resultados obtenidos y publicados han sido desarrollados de forma numérica y experimental, validándose el método de trabajo y dando consistencia a las soluciones propuestas.[CA] La capacitat de controlar i modificar els feixos d'energia ha sigut motiu d'investigació per part de la comunitat científica des de llarg temps arrere. En el camp de l'acústica, este control energètic de les ones mecàniques té nombroses aplicacions. Des de les aplicacions industrials, alimentàries, farmacèutiques, etcètera fins la biomedicina. Esta tesi es basa en l'aplicació del control i modulació focal dels ultrasons per a l'ús en este últim camp. Es pot modular i controlar els focus d'ultrasons de diferents formes. En este cas, s'han desenvolupat lents planes que utilitzen el principi de la difracció per a aconseguir focalitzar els feixos. Els avantatges de l'ús de lents planes de focalització permeten ser implementades de forma senzilla en processos de mecanització i inclús per mitjà d'impressió 3D. Es proposa utilitzar transductores plans que a l'emetre sobre una lent acústica, es produïsca una conformació focal de característiques controlades. La lent coneguda com a lent de Fresnel (FZP) ha sigut triada com a base de disseny en la implementació de les diferents solucions que aconseguixen complir amb els objectius marcats. Per mitjà de l'aplicació de modificacions en una FZP es pot aconseguir passar d'una lent amb capacitats extraordinàries de focalització a una lent capaç de controlar la resolució lateral i la profunditat de focus i inclús millorar el guany. L'objectiu final d'aplicació és l'ús en transductores d'ultrasons d'alta intensitat coneguts com HIFU. Millorar la capacitat de resolució fa que es puguen desenvolupar millors teràpies oncològiques que suposen un índex major d'èxit en la lluita contra el càncer. En la present tesi s'ha proposat, a més, una nova lent FZP basada en el canvi de fase que pot resultar un abans i un després en aplicacions biomèdiques. S'ha aconseguit no sols millorar l'eficiència d'una FZP, sinó que s'ha aconseguit implementar en materials compatibles amb ressonància magnètica. S'han desenvolupat models numèrics basats en el mètode dels elements finits que emulen la física involucrada. Les mesures han sigut realitzades en condicions controlades per un sistema robotitzat d'alta precisió. Tots els resultats obtinguts i publicats han sigut desenvolupats de forma numèrica i experimental, validant-se el mètode de treball i donant consistència a les solucions proposades.[EN] The ability to control and modify energy beams has been the subject of research by the scientific community for a long time. In the acoustic field, this energetic control of mechanical waves has numerous applications. From industrial, food, pharmaceutical applications, et cetera, to biomedicine. This thesis is based on the ultrasound control and focal modulation applications. It is possible to modulate and control the ultrasound focii in different ways. In this case, flat lenses were developed based on the principle of diffraction to focus the beams. The advantages of using flat focusing lenses allow them to be easily implemented in machining and drilling processes and even through 3D printing. It was proposed to use planar transducers that when emitting on an acoustic lens, controlled characteristics of focal conformation were produced. The lens known as Fresnel Zone Plane (FZP) was chosen as the implementation design basis for the different solutions that manage to fulfill the objectives set. By applying modifications to an FZP it was possible to go from a lens with extraordinary focusing capabilities to a lens that was capable to control lateral resolution, depth of focus and even improving the gain. The final objective application was the use in high intensity ultrasound transducers known as HIFU. Improving the ability to resolve makes it possible to develop better cancer therapies that represent a higher rate of success in the fight against cancer. In the present thesis, a novel FZP lens based on phase change has also been proposed that can be a before and after in biomedical applications. It has not only been possible to improve the efficiency of an FZP, but it has also been possible to implement it in materials compatible with magnetic resonance imaging. Numerical models based on the finite element method were developed for emulating the involved physics. Measurements were carried out under controlled conditions by a high precision robotic system. All the results obtained and published were developed numerically and experimentally, validating the working method and giving consistency to the proposed solutions.I want to acknowledge the following public funding sources that have made possible this research: Grant BES-2016-077133 (Ministerio de Ciencia, Innovación y Universidades de España) Project TEC2015-70939-R (MINECO/FEDER). Tomsk Polytechnic University within the framework of Tomsk Polytechnic University Competitiveness Enhancement Program.Tarrazó Serrano, D. (2020). Design, modelling, characterization and implementation of acoustic lenses for modulation of ultrasound beams [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159895TESISCompendi