3,716 research outputs found
Acoustic scattering by an inhomogeneous layer on a rigid plate
The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data
A finite element surface impedance representation for steady-state problems
A procedure for determining the scattered pressure field resulting from a monochromatic harmonic wave that is incident upon a layer energy absorbing structure is treated. The situation where the structure is modeled with finite elements and the surrounding acoustic medium (water or air) is represented with either acoustic finite elements, or some type of boundary integral formulation, is considered. Finite element modeling problems arise when the construction of the structure, at the fluid structure interface, are nonhomogeneous and in particular, when the inhomogeneities are small relative to the acoustic wave length. An approximate procedure is presented for replacing the detailed microscopic representation of the layered surface configuration with an equivalent simple surface impedance finite element, which is especially designed to work only at limited frequencies. An example problem is presented using NASTRAN. However, the procedure is general enough to adapt to practically any finite element code having a steady state option
Incorporation of macroscopic heterogeneity within a porous layer to enhance its acoustic absorptance
We seek the response, in particular the spectral absorptance, of a
rigidly-backed periodically-(in one horizontal~~ direction) ~inhomogeneous
~layer ~composed ~of ~alternating rigid and macroscopically-homogeneous porous
portions, submitted to an airborne acoustic plane body wave. The rigorous
theory of this problem is given and the means by which the latter can be
numerically solved are outlined. At low frequencies, a suitable approximation
derives from one linear equation in one unknown. This approximate solution is
shown to be equivalent to that of the problem of the same wave incident on a
homogeneous, isotropic layer. The thickness of this layer is identical to
that of the inhomogeneous layer, the effective complex body wave velocity
therein is identical to that of the porous portion of the inhomogeneous layer,
but the complex effective mass density, whose expression is given in explicit
algebraic form, is that of the reference homogeneous macroscopically-porous
layer divided by the filling factor (fraction of porous material to the total
material in one grating period). This difference of density is the reason why
it is possible for the lowest-frequency absorptance peak to be higher than that
of a reference layer. Also, it is shown how to augment the height of this peak
so that it attains unity (i.e., total absorption) and how to shift it to lower
frequencies, as is required in certain applications
Elastic Wave Eigenmode Solver for Acoustic Waveguides
A numerical solver for the elastic wave eigenmodes in acoustic waveguides of
inhomogeneous cross-section is presented. Operating under the assumptions of
linear, isotropic materials, it utilizes a finite-difference method on a
staggered grid to solve for the acoustic eigenmodes of the vector-field elastic
wave equation. Free, fixed, symmetry, and anti-symmetry boundary conditions are
implemented, enabling efficient simulation of acoustic structures with
geometrical symmetries and terminations. Perfectly matched layers are also
implemented, allowing for the simulation of radiative (leaky) modes. The method
is analogous to eigenmode solvers ubiquitously employed in electromagnetics to
find waveguide modes, and enables design of acoustic waveguides as well as
seamless integration with electromagnetic solvers for optomechanical device
design. The accuracy of the solver is demonstrated by calculating
eigenfrequencies and mode shapes for common acoustic modes in several simple
geometries and comparing the results to analytical solutions where available or
to numerical solvers based on more computationally expensive methods
Engineering non-Hermitian and topological flow of sound
During the last decades, acoustic and phononic metamaterial research was focused
on finding new ways to modify the flow of sound waves at will. In this project,
we focus on exploring novel properties of sound by developing numerical code and
theoretical methods to understand the acoustic analogy to non-Hermitian systems,
topological insulators, and other exciting phenomena in condensed matter physics
such as the magic angle in twisted bilayer graphene. Succinctly, we wish to translate
these common notions of quantum mechanics into classical acoustics to find new
properties for the case of sound.
Non-Hermitian acoustic structures can be achieved by balancing acoustic loss and
gain units. Commonly known as Parity-Time (PT) symmetric structures, they have
neither parity symmetry nor time-reversal symmetry, but are nevertheless symmetric
in the product of both. In particular, the doctoral research project aims at designing
acoustic PT symmetry and demonstrating the extraordinary scattering characteristics
of the acoustic PT medium based on exact theoretical predictions and numerical
analysis. Hence, we investigate the possibilities to realize one-way cloaks of invisibility
and broken symmetry properties with amplifying or attenuating behaviour.
Topological sound combines the knowledge of topology in mathematics and electronics
with sound waves. Knowing that artificial sonic lattices have been widely used
to explore topological phases of sound and its properties, we propose to study the
properties of Second Order Topological Insulators when non-hermiticity is involved.
Deriving a semi-numerical tool that allows us to compute the spectral dependence
of corner states in the presence of defects, we illustrate the limits of the topological
resilience of the confined non-Hermitian acoustic states.
An attractive motivation of these acoustic structures compared to their electronic
counterparts, is their easy fabrication and tunability, allowing the experimental
verification of this quantum analogies as well as the development of many numerical
studies. Thereby, in the last part of this thesis we mimic twisted bilayer physics in a
mechanical twisted bilayer configuration and also in an acoustical bilayer. Designing
the mathematical models to describe the physics involved, we show how the twist
angle is related to the flat band formation as happens in twisted bilayer graphene.Programa de Doctorado en Ciencia e Ingeniería de Materiales por la Universidad Carlos III de MadridPresidente: Ramón Eulalio Zaera Polo.- Secretario: Clivia Marfa Sotomayor Torres.- Vocal: José Vicente Álvarez Carrer
Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material
International audienceWave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives
Gradient index phononic crystals and metamaterials
Phononic crystals and acoustic metamaterials
are periodic structures whose effective properties can be
tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible
to locally change the properties of a finite crystal in such
a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be
accurately described by means of ray theory, and different refractive devices can be designed in the framework of
wave propagation in inhomogeneous media. In this paper
we review the different devices that have been studied for
the control of both bulk and guided acoustic waves based
on graded phononic crystals
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