596 research outputs found
Parabolic Metamaterials and Dirac Bridges
A new class of multi-scale structures, referred to as `parabolic
metamaterials' is introduced and studied in this paper. For an elastic
two-dimensional triangular lattice, we identify dynamic regimes, which
corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such
regimes lead to a highly localised and focussed unidirectional beam when the
lattice is excited. We also show that the flexural rigidities of elastic
ligaments are essential in establishing the `parabolic metamaterial' regimes.Comment: 14 pages, 4 figure
Active cloaking of finite defects for flexural waves in elastic plates
We present a new method to create an active cloak for a rigid inclusion in a
thin plate, and analyse flexural waves within such a plate governed by the
Kirchhoff plate equation. We consider scattering of both a plane wave and a
cylindrical wave by a single clamped inclusion of circular shape. In order to
cloak the inclusion, we place control sources at small distances from the
scatterer and choose their intensities to eliminate propagating orders of the
scattered wave, thus reconstructing the respective incident wave. We then vary
the number and position of the control sources to obtain the most effective
configuration for cloaking the circular inclusion. Finally, we successfully
cloak an arbitrarily shaped scatterer in a thin plate by deriving a
semi-analytical, asymptotic algorithm.Comment: 19 pages, 14 figures, 1 tabl
Achieving control of in-plane elastic waves
We derive the elastic properties of a cylindrical cloak for in-plane coupled
shear and pressure waves. The cloak is characterized by a rank 4 elasticity
tensor with 16 spatially varying entries which are deduced from a geometric
transform. Remarkably, the Navier equations retain their form under this
transform, which is generally untrue [Milton et al., New J. Phys. 8, 248
(2006)]. We numerically check that clamped and freely vibrating obstacles
located inside the neutral region are cloaked disrespectful of the frequency
and the polarization of an incoming elastic wave.Comment: 9 pages, 4 figure
Eigenvalue problem in a solid with many inclusions: asymptotic analysis
We construct the asymptotic approximation to the first eigenvalue and
corresponding eigensolution of Laplace's operator inside a domain containing a
cloud of small rigid inclusions. The separation of the small inclusions is
characterised by a small parameter which is much larger compared with the
nominal size of inclusions. Remainder estimates for the approximations to the
first eigenvalue and associated eigenfield are presented. Numerical
illustrations are given to demonstrate the efficiency of the asymptotic
approach compared to conventional numerical techniques, such as the finite
element method, for three-dimensional solids containing clusters of small
inclusions.Comment: 55 pages, 5 figure
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