Acoustic scattering in a waveguide with a height discontinuity bridged by a membrane: a tailored Galerkin approach

Abstract

An arterial dissection is a longitudinal tear in the vessel wall, which can create a false lumen for blood flow and may propagate quickly, leading to death. We employ a computational model for a dissection using the extended finite element method with a cohesive traction-separation law for the tear faces. The arterial wall is described by the anisotropic hyperelastic Holzapfel-Gasser-Ogden material model that accounts for collagen fibres and ground matrix, while the evolution of damage is governed by a linear cohesive traction-separation law. We simulate propagation in both peeling and pressure-loading tests. For peeling tests, we consider strips and discs cut from the arterial wall. Propagation is found to occur preferentially along the material axes with the greatest stiffness, which are determined by the fibre orientation. In the case of pressure-driven propagation, we examine a cylindrical model, with an initial tear in the shape of an arc. Long and shallow dissections lead to buckling of the inner wall between the true lumen and the dissection. The various buckling configurations closely match those seen in clinical CT scans. Our results also indicate that a deeper tear is more likely to propagate.

Guided wave propagation in cylindrical ducts with elastic walls enclosing a fluid moving with a uniform velocity

“…For example, modes are seen to transfer their energy from the structure to the fluid, and vice versa, as the frequency is increased. This illustrates the complexity of this type of coupled guided wave problem and this is behaviour that has been shown before [13]. Of course, it is also well known that the compressional modes never cross one another in the dispersion curves of a lossless system, and instead they avoid crossing, or veer apart, as the energy is transferred between the fluid and the structure [12,21].…”

“…For example, Choy and Huang [2] demonstrate the influence of a uniform mean flow on the characteristics of their membrane based drumlike silencer. However, very few articles examine the effects of mean flow on duct wall vibrations, with only the numerical approach of Kirby and Cummings [13], and the analytic methods of Martin [14] being relevant to this current study. Instead, the majority of investigations focus on the influence of mean flow on the vibro-acoustic behaviour of plates.…”

An Efficient Semi-Analytical Scheme for Determining the Reflection of Lamb Waves in a Semi-Infinite Elastic Waveguide

“…This is essentially due to the Gibbs phenomenon. There are a variety of numerical treatments that can be applied in this and other waveguide problems to aid convergence, including the Lanczos σ-approximation (see, e.g., [13,14]).…”

Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide

“…To be precise, provided sufficient terms are taken, the pressure and mean velocity are guaranteed to agree with a high level of accuracy at the matching interface, whereas the agreement between the normal velocities depends on the strength of the singularity in the velocity field, see, e.g. [30,31]. As far as the authors are aware, a valid analytic mode-matching procedure has not appeared in the literature for EP conditions, and one of the main purposes of this article is to extend the method to these situations.…”