An Ultrasonic Lens Design Based on Prefractal Structures

Castiñeira-Ibáñez, Sergio; Tarrazó-Serrano, Daniel; Candelas, Pilar; Rubio, Constanza

doi:10.3390/sym8040028

Cited by 8 publications

(6 citation statements)

References 14 publications

(13 reference statements)

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“…If a 3D model is considered, this will require high computational resources. To simplify the model and reduce this computational cost, as shown in previous works [19,20], the geometrical properties of the model are used taking advantage of its axisymmetry. Therefore, the model is simplified by implementing a semi-lens only.…”

Section: Numerical Modelmentioning

confidence: 99%

MRI Compatible Planar Material Acoustic Lenses

et al. 2018

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Zone plate lenses are used in many areas of physics where planar geometry is advantageous in comparison with conventional curved lenses. There are several types of zone plate lenses, such as the well-known Fresnel zone plates (FZPs) or the more recent fractal and Fibonacci zone plates. The selection of the lens material plays a very important role in beam modulation control. This work presents a comparison between FZPs made from different materials in the ultrasonic range in order to use them as magnetic resonance imaging (MRI) compatible materials. Three different MRI compatible polymers are considered: Acrylonitrile butadiene styrene (ABS), polymethyl methacrylate (PMMA) and polylactic acid (PLA). Numerical simulations based on finite elements method (FEM) and experimental results are shown. The focusing capabilities of brass lenses and polymer zone plate lenses are compared.

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Section: Numerical Modelmentioning

confidence: 99%

MRI Compatible Planar Material Acoustic Lenses

et al. 2018

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“…As it has been presented in previous works [19,20], the following boundary conditions have been defined: the PCFL is considered infinitely rigid marking the contours of the elements applying the Newmann condition (the sound velocity in the contour is zero). The contours of the model are defined as wave radiation condition boundaries to emulate an infinitely large medium and therefore the Sommerfeld condition is satisfied.…”

Section: Methodsmentioning

confidence: 99%

Numerical simulation and laboratory measurements on the influence of fractal dimension on the acoustic beam modulation of a Polyadic Cantor Fractal lenses

et al. 2019

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The possibility of modulating the ultrasound beam produced by a transducer through lenses has become an important task. The fact that these lenses are flat, facilitates their design, construction and applications. If, in addition, the design itself incorporates geometries that affect differently the foci profile on the axial axis of the lens, improvements become more significant. In this work the design of a flat lens based on a Polyadic Cantor fractal geometries is presented. The influence of the so-called fractal dimension on the modulation of the ultrasonic beam to obtain the foci is analysed. In this paper, experimental results under controlled conditions are presented. The numerical solutions obtained have been validated.

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“…Although interest in fractals has increased following Mandelbrot's work [2] their application to physical systems remains at best problematic. Practical application of fractals remains somewhat limited and references [3][4][5][6][7][8][9] provide a snapshot of what is evidently far from mainstream use. The difficulty with fractals stems from an inability to quantify traditional measures of volume, area and length and consequently, traditional mechanics is not possible.…”

Section: Introductionmentioning

confidence: 99%

A tessellated continuum approach for the static analysis of perforated structures

Davey

Darvizeh

Sedqi

2020

Computers & Structures

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Pre-fractals have the capacity to represent structures of different levels of complexity and have recently been shown to be suitable for continuum analysis using a method called tessellated continuum mechanics. Tessellated continuum mechanics is an analytical theory for the analysis of porous/perforated structures but presently has only been tested to any extent on heat transfer problems.This paper is concerned with extending the implementation of the tessellated approach to static structural analysis of one and two dimensions with a particular emphasis on perforated plates. The principal objective of the work is to establish that the structural analysis of perforated structures is possible to a very high degree of accuracy in a continuum mechanics framework. The tessellated approach involves the local expansion of space to close perforations and invokes the concept of finite similitude, which has appeared in the recent literature.The consequences of local-space scaling are examined and static testing for beams and plates, constrained by different boundary conditions are presented.

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An Ultrasonic Lens Design Based on Prefractal Structures

Cited by 8 publications

References 14 publications

MRI Compatible Planar Material Acoustic Lenses

MRI Compatible Planar Material Acoustic Lenses

Numerical simulation and laboratory measurements on the influence of fractal dimension on the acoustic beam modulation of a Polyadic Cantor Fractal lenses

A tessellated continuum approach for the static analysis of perforated structures

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