Dispersion of waves and transmission–reflection in blood vessels with structured stents

Frecentese, S.; Papathanasiou, Theodosios K.; Movchan, A. B.; Movchan, N. V.

doi:10.1098/rspa.2018.0816

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…Despite the horizontal and vertical extents of the slab in Figure 3 being finite, the dispersive properties of bulk aluminium, and of the infinite periodic microstructured constituent, provide invaluable information for wave scattering phenomena within a finite structure. Previous studies, also using Bloch-Floquet quasi-periodicity to derive dispersions surfaces from which interesting frequencies were identified for finite substructures, have been carried out in several research fields, including civil [39,40] and biomedical [41,42] engineering.…”

Section: Resultsmentioning

confidence: 99%

Trapped Modes and Negative Refraction in a Locally Resonant Metamaterial: Transient Insights into Manufacturing Bounds for Ultrasonic Applications

Tallarico

Haslinger

2021

Applied Sciences

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The transient scattering of in-plane elastic waves from a finite-sized periodic structure, comprising a regular grid of Swiss-cross holes arranged according to a square lattice, is considered. The theoretical and numerical modelling focuses on the unexplored ultrasonic frequency regime, well beyond the first, wide, locally resonant band-gap of the structure. Dispersive properties of the periodic array, determined by Bloch–Floquet analysis, are used to identify candidates for high-fidelity GPU-accelerated transient scattering simulations. Several unusual wave phenomena are identified from the simulations, including negative refraction, focusing, partial cloaking, and wave trapping. The transient finite element modelling framework offers insights on the lifetimes of such phenomena for potential practical applications. In addition, nonideal counterparts with rough edges are modelled using characteristic statistical parameters commonly observed in additive manufacturing. The analysis shows that the identified wave effects appear likely to be robust with respect to potential manufacturing uncertainties in future studies.

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Section: Resultsmentioning

confidence: 99%

Trapped Modes and Negative Refraction in a Locally Resonant Metamaterial: Transient Insights into Manufacturing Bounds for Ultrasonic Applications

Tallarico

Haslinger

2021

Applied Sciences

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“…Only in this case is the pipe stiffness or thickness properties vary periodically. Of course, modulations of pipe stiffness or thickness can produce enhanced transmission loss even when a single pipe is used [ 16 , 17 ]. A key hypothesis of the present study is that synergies between pipe modulation inducing reflection and destructive interference from parallel branches could yield very good attenuation features.…”

Section: Introductionmentioning

confidence: 99%

The Herschel-Quincke tube with modulated branches

Papathanasiou

Tsolakis

Spitas

et al. 2022

Phil. Trans. R. Soc. A.

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The Herschel-Quincke (HQ) tube concept for transmission loss in pipe systems is expanded to include cases of branches with modulated properties. Modulated waveguides, featuring corrugations in their geometry or speed of sound, are known to produce significant reflection even without the parallel branch of the HQ tube. The HQ tube, in its classical form, produces narrow banded transmission loss at frequencies related to the length, wavenumber and cross-section area of the parallel branch. The modulated Herschel-Quincke (MHQ) tube combines these attributes to produce enhanced transmission loss characteristics in terms of both width and number of transmission loss bands. Several modulated profiles for the speed of sound in different branches of the tube are considered and analytical expressions for the transmission loss and resonant conditions are derived. Detailed analysis of periodically stratified branch profiles demonstrates the effectiveness of the MHQ tube for fluid-borne noise attenuation in pipe systems. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

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“…Studying gBBMB on a network with variable coefficients can therefore also help us understand how stents affect flow in the arterial tree. The analysis of blood flow in stented vessels has attracted considerable attention: [10,11,17,18,28] describe several different perspectives on analytical and numerical aspects of stent modelling. Now, when the artery under consideration is very long, the use of a dispersive PDE such as gBBMB as a blood flow model is particularly well-justified: in order for dispersion to be an important influence on the movement of some material continuum, there must be enough room to let waves disperse.…”

Section: Introductionmentioning

confidence: 99%

A Mass-Conserving Formulation of the Generalized Benjamin-Bona-Mahony-Burgers Equation on Star Networks

Morgan

2021

Preprint

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The generalized Benjamin-Bona-Mahony-Burgers equation (gBBMB) describes the flow of blood through a long, viscoelastic artery. In this article we introduce a formulation of gBBMB valid on networks with semi-infinite edges joined at a single junction, with the network's edges corresponding to a segment of the arterial tree. To reflect sudden changes in the material properties of blood vessels, the coefficients of gBBMB are allowed to take different values on each edge of the network. Critically, our formulation ensures that the total mass of the solution to gBBMB is constant in time, even in the presence of dissipation. We also establish local-in-time well-posedness of this new formulation for sufficiently regular initial data. Then, we show how energy methods can be used to extend the local solution to a solution valid for all positive times, provided certain constraints are imposed on the parameters of the model PDE and the network. To build intuition for how waves scatter off the central junction of a network with two edges, we demonstrate the results of some numerical simulations.

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Dispersion of waves and transmission–reflection in blood vessels with structured stents

Cited by 6 publications

References 25 publications

Trapped Modes and Negative Refraction in a Locally Resonant Metamaterial: Transient Insights into Manufacturing Bounds for Ultrasonic Applications

Trapped Modes and Negative Refraction in a Locally Resonant Metamaterial: Transient Insights into Manufacturing Bounds for Ultrasonic Applications

The Herschel-Quincke tube with modulated branches

A Mass-Conserving Formulation of the Generalized Benjamin-Bona-Mahony-Burgers Equation on Star Networks

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