9,081 research outputs found
Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets
We start by a review of the chronology of mathematical results on the
Dirichlet-to-Neumann map which paved the way towards the physics of
transformational acoustics. We then rederive the expression for the
(anisotropic) density and bulk modulus appearing in the pressure wave equation
written in the transformed coordinates. A spherical acoustic cloak consisting
of an alternation of homogeneous isotropic concentric layers is further
proposed based on the effective medium theory. This cloak is characterised by a
low reflection and good efficiency over a large bandwidth for both near and far
fields, which approximates the ideal cloak with a inhomogeneous and anisotropic
distribution of material parameters. The latter suffers from singular material
parameters on its inner surface. This singularity depends upon the sharpness of
corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak
becomes more and more singular when the number of vertices increases if it is
star shaped. We thus analyse the acoustic response of a non-singular spherical
cloak designed by blowing up a small ball instead of a point, as proposed in
[Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The
multilayered approximation of this cloak requires less extreme densities
(especially for the lowest bound). Finally, we investigate another type of
non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev.
Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion.
OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110)
Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic
optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices;
(160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility;
(230.3205) Invisibility cloak
Compressive Matched-Field Processing
Source localization by matched-field processing (MFP) generally involves
solving a number of computationally intensive partial differential equations.
This paper introduces a technique that mitigates this computational workload by
"compressing" these computations. Drawing on key concepts from the recently
developed field of compressed sensing, it shows how a low-dimensional proxy for
the Green's function can be constructed by backpropagating a small set of
random receiver vectors. Then, the source can be located by performing a number
of "short" correlations between this proxy and the projection of the recorded
acoustic data in the compressed space. Numerical experiments in a Pekeris ocean
waveguide are presented which demonstrate that this compressed version of MFP
is as effective as traditional MFP even when the compression is significant.
The results are particularly promising in the broadband regime where using as
few as two random backpropagations per frequency performs almost as well as the
traditional broadband MFP, but with the added benefit of generic applicability.
That is, the computationally intensive backpropagations may be computed offline
independently from the received signals, and may be reused to locate any source
within the search grid area
Acoustic source localization : exploring theory and practice
Over the past few decades, noise pollution became an important issue in modern society. This has led to an increased effort in the industry to reduce noise. Acoustic source localization methods determine the location and strength of the vibrations which are the cause of sound based onmeasurements of the sound field. This thesis describes a theoretical study of many facets of the acoustic source localization problem as well as the development, implementation and validation of new source localization methods. The main objective is to increase the range of applications of inverse acoustics and to develop accurate and computationally efficient methods for each of these applications. Four applications are considered. Firstly, the inverse acoustic problem is considered where the source and the measurement points are located on two parallel planes. A new fast method to solve this problem is developed and it is compared to the existing method planar nearfield acoustic holography (PNAH) from a theoretical point of view, as well as by means of simulations and experiments. Both methods are fast but the newmethod yields more robust and accurate results. Secondly, measurements in inverse acoustics are often point-by-point or full array measurements. However a straightforward and cost-effective alternative to these approaches is a sensor or array which moves through the sound field during the measurement to gather sound field information. The same numerical techniques make it possible to apply inverse acoustics to the case where the source moves and the sensors are fixed in space. It is shown that the inverse methods such as the inverse boundary element method (IBEM) can be applied to this problem. To arrive at an accurate representation of the sound field, an optimized signal processing method is applied and it is shown experimentally that this method leads to accurate results. Thirdly, a theoretical framework is established for the inverse acoustical problem where the sound field and the source are represented by a cross-spectral matrix. This problem is important in inverse acoustics because it occurs in the inverse calculation of sound intensity. The existing methods for this problem are analyzed from a theoretical point of view using this framework and a new method is derived from it. A simulation study indicates that the new method improves the results by 30% in some cases and the results are similar otherwise. Finally, the localization of point sources in the acoustic near field is considered. MUltiple SIgnal Classification (MUSIC) is newly applied to the Boundary element method (BEM) for this purpose. It is shown that this approach makes it possible to localize point sources accurately even if the noise level is extremely high or if the number of sensors is low
Nonlinear modes of clarinet-like musical instruments
The concept of nonlinear modes is applied in order to analyze the behavior of
a model of woodwind reed instruments. Using a modal expansion of the impedance
of the instrument, and by projecting the equation for the acoustic pressure on
the normal modes of the air column, a system of second order ordinary
differential equations is obtained. The equations are coupled through the
nonlinear relation describing the volume flow of air through the reed channel
in response to the pressure difference across the reed. The system is treated
using an amplitude-phase formulation for nonlinear modes, where the frequency
and damping functions, as well as the invariant manifolds in the phase space,
are unknowns to be determined. The formulation gives, without explicit
integration of the underlying ordinary differential equation, access to the
transient, the limit cycle, its period and stability. The process is
illustrated for a model reduced to three normal modes of the air column
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