687 research outputs found
Elastodynamic cloaking and field enhancement for soft spheres
In this paper, we bring to the awareness of the scientific community and
civil engineers, an important fact: the possible lack of wave protection of
transformational elastic cloaks. To do so, we propose spherical cloaks
described by a non-singular asymmetric elasticity tensor depending upon a small
parameter that defines the softness of a region one would like to
conceal from elastodynamic waves. By varying , we generate a class of
soft spheres dressed by elastodynamic cloaks, which are shown to considerably
reduce the soft spheres' scattering. Importantly, such cloaks also provide some
wave protection except for a countable set of frequencies, for which some large
elastic field enhancement (resonance peaks) can be observed within the cloaked
soft spheres, hence entailing a possible lack of wave protection. We further
present an investigation of trapped modes in elasticity via which we supply a
good approximation of such Mie-type resonances by some transcendental equation.
Next, after a detailed presentation of spherical elastodynamic PML of Cosserat
type, we introduce a novel generation of cloaks, the mixed cloaks, as a
solution to the lack of wave protection in elastodynamic cloaking. Indeed,
mixed cloaks achieve both invisibility cloaking and protection throughout a
large range of frequencies. We think, mixed cloaks will soon be generalized to
other areas of physics and engineering and will in particular foster studies in
experiments.Comment: V2: major changes. More details on the study of trapped modes in
elasticity. Mixed cloaks introduced. Latex files, 27 pages, 14 figures. The
last version will appear at Journal of Physics D: Applied Physics.
Pacs:41.20.Jb,42.25.Bs,42.70.Qs,43.20.Bi,43.25.Gf. arXiv admin note: text
overlap with arXiv:1403.184
Cloaking via change of variables in elastic impedance tomography
We discuss the concept of cloaking for elastic impedance tomography, in
which, we seek information on the elasticity tensor of an elastic medium from
the knowledge of measurements on its boundary. We derive some theoretical
results illustrated by some numerical simulations.Comment: latex, 2 figures, 11 pages, submitte
Controlling solid elastic waves with spherical cloaks
We propose a cloak for coupled shear and pressure waves in solids. Its
elastic properties are deduced from a geometric transform that retains the form
of Navier equations. The spherical shell is made of an anisotropic and
heterogeneous medium described by an elasticity tensor C' (without the minor
symmetries) which has 21 non-zero spatially varying coefficients in spherical
coordinates. Although some entries of C, e.g. some with a radial subscript, and
the density (a scalar radial function) vanish on the inner boundary of the
cloak, this metamaterial exhibits less singularities than its cylindrical
counterpart studied in [M. Brun, S. Guenneau, A.B. Movchan, Appl. Phys. Lett.
94, 061903 (2009).]
In the latter work, C' suffered some infinite entries, unlike in our case.
Finite element computations confirm that elastic waves are smoothly detoured
around a spherical void without reflection.Comment: Version 3: minor typos corrected. Figures captions improved. 5
figures. Key words: 3D elastic cloaking, seismic metamaterials. This paper is
the cover of the 14 July 2014 issue of Applied Physics Letter
Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates
We present in this paper a theoretical and numerical analysis of bending
waves localized on the boundary of a platonic crystal whose building blocks are
split ring resonators (SRR). We first derive the homogenized parameters of the
structured plate using a three-scale asymptotic expansion in the linearized
biharmonic equation. In the limit when the wavelength of the bending wave is
much larger than the typical heterogeneity size of the platonic crystal, we
show that it behaves as an artificial plate with an anisotropic effective Young
modulus and a dispersive effective mass density. We then analyze dispersion
diagrams associated with bending waves propagating within an infinite array of
SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves.
We finally demonstrate that this structure displays the hallmarks of
All-Angle-Negative-Refraction(AANR) and it leads to superlensing and
ultrarefraction effects, interpreted thanks to our homogenization model as a
consequence of negative and vanishing effective density, respectively.Comment: 17 pages, 6 figure
Steering in-plane shear waves with inertial resonators in platonic crystals
Numerical simulations shed light on control of shear elastic wave propagation
in plates structured with inertial resonators. The structural element is
composed of a heavy core connected to the main freestanding plate through tiny
ligaments. It is shown that such a configuration exhibits a complete band gap
in the low frequency regime. As a byproduct, we further describe the asymmetric
twisting vibration of a single scatterer via modal analysis, dispersion and
transmission loss. This might pave the way to new functionalities such as
focusing and self-collimation in elastic plates
High-frequency homogenization of zero frequency stop band photonic and phononic crystals
We present an accurate methodology for representing the physics of waves, for
periodic structures, through effective properties for a replacement bulk
medium: This is valid even for media with zero frequency stop-bands and where
high frequency phenomena dominate. Since the work of Lord Rayleigh in 1892, low
frequency (or quasi-static) behaviour has been neatly encapsulated in effective
anisotropic media. However such classical homogenization theories break down in
the high-frequency or stop band regime.
Higher frequency phenomena are of significant importance in photonics
(transverse magnetic waves propagating in infinite conducting parallel fibers),
phononics (anti-plane shear waves propagating in isotropic elastic materials
with inclusions), and platonics (flexural waves propagating in thin-elastic
plates with holes). Fortunately, the recently proposed high-frequency
homogenization (HFH) theory is only constrained by the knowledge of standing
waves in order to asymptotically reconstruct dispersion curves and associated
Floquet-Bloch eigenfields: It is capable of accurately representing
zero-frequency stop band structures. The homogenized equations are partial
differential equations with a dispersive anisotropic homogenized tensor that
characterizes the effective medium.
We apply HFH to metamaterials, exploiting the subtle features of Bloch
dispersion curves such as Dirac-like cones, as well as zero and negative group
velocity near stop bands in order to achieve exciting physical phenomena such
as cloaking, lensing and endoscope effects. These are simulated numerically
using finite elements and compared to predictions from HFH. An extension of HFH
to periodic supercells enabling complete reconstruction of dispersion curves
through an unfolding technique is also introduced
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