666 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
Propagation and filtering of elastic and electromagnetic waves in piezoelectric composite structures
In this article we discuss the modelling of elastic and electromagnetic wave
propagation through one- and two-dimensional structured piezoelectric solids.
Dispersion and the effect of piezoelectricity on the group velocity and
positions of stop bands are studied in detail. We will also analyze the
reflection and transmission associated with the problem of scattering of an
elastic wave by a heterogeneous piezoelectric stack. Special attention is given
to the occurrence of transmission resonances in finite stacks and their
dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric
checkerboard structure is subsequently introduced, for which the dispersion
surfaces for Bloch waves have been constructed and analysed, with the emphasis
on the dynamic anisotropy and special features of standing waves within the
piezoelectric structure.Comment: 24 pages, 18 figures, 3 tables. Preprint version of a research
article, accepted for publication in "Mathematical Methods in the Applied
Science (2016)
Edge waves and localisation in lattices containing tilted resonators
The paper presents the study of waves in a structured geometrically chiral
solid. A special attention is given to the analysis of the Bloch-Floquet waves
in a doubly periodic high-contrast lattice containing tilted resonators.
Dirac-like dispersion of Bloch waves in the structure is identified, studied
and applied to wave-guiding and wave-defect interaction problems. The work is
extended to the transmission problems and models of fracture, where
localisation and edge waves occur. The theoretical derivations are accompanied
with numerical simulations and illustrations
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
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