17 research outputs found
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
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)
Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures
In this paper, we show that the transient waveforms arising from several
localised pulses in a micro-structured material can be reproduced by a
corresponding generalised continuum of the relaxed micromorphic type.
Specifically, we compare the dynamic response of a bounded micro-structured
material to that of bounded continua with special kinematic properties: (i) the
relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic
continuum. We show that, while the Cauchy theory is able to describe the
overall behaviour of the metastructure only at low frequencies, the relaxed
micromorphic model goes far beyond by giving a correct description of the pulse
propagation in the frequency band-gap and at frequencies intersecting the
optical branches. In addition, we observe a computational time reduction
associated with the use of the relaxed micromorphic continuum, compared to the
sensible computational time needed to perform a transient computation in a
micro-structured domain
Relaxed micromorphic broadband scattering for finite-size meta-structures -- a detailed development
The conception of new metamaterials showing unorthodox behaviors with respect
to elastic wavepropagation has become possible in recent years thanks to
powerful dynamical homogenization techniques. Such methods effectively allow to
describe the behavior of an infinite medium generated by periodically
architectured base materials. Nevertheless, when it comes to the study of the
scattering properties of finite-sized structures, dealing with the correct
boundary conditions at the macroscopicscale becomes challenging. In this paper,
we show how finite-domain boundary value problems canbe set-up in the framework
of enriched continuum mechanics (relaxed micromorphic model) by imposing
continuity of macroscopic displacement and of generalized traction when
non-local effects areneglected.The case of a metamaterial slab of finite width
is presented, its scattering properties are studied viaa semi-analytical
solution of the relaxed micromorphic model and compared to numerical
simulationsencoding all details of the selected microstructure. The reflection
coefficient obtained via the twomethods is presented as a function of the
frequency and of the direction of propagation of the incidentwave. We find
excellent agreement for a large range of frequencies going from the long-wave
limitto frequencies beyond the first band-gap and for angles of incidence
ranging from normal to nearparallel incidence. The case of a semi-infinite
metamaterial is also presented and is seen to be areliable measure of the
average behavior of the finite metastructure. A tremendous gain in termsof
computational time is obtained when using the relaxed micromorphic model for
the study of theconsidered metastructure
Towards the conception of complex engineering meta-structures: relaxed-micromorphic modelling of mechanical diodes
In this paper we show that an enriched continuum model of the micromorphic
type (Relaxed Micromorphic Model) can be safely used to model metamaterials'
response in view of their use for meta-structural design. We focus on the fact
that the reduced model's structure, coupled with the introduction of well-posed
interface conditions, allows us to easily test different combinations of
metamaterials' and classical-materials bricks, so that we can eventually end-up
with the conception of a meta-structure acting as a mechanical diode for
low/medium frequencies and as a total screen for higher frequencies. Thanks to
the reduced model's structure, we are also able to optimize this meta-structure
so that the diode-behaviour is enhanced for both "pressure" and "shear"
incident waves and for all possible angles of incidence.Comment: 19 pages, 18 figures (43 pictures). arXiv admin note: substantial
text overlap with arXiv:2007.1494
Relaxed micromorphic broadband scattering for finite-size meta-structures - a detailed development
The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe the behavior of an infinite medium generated by periodically architectured base materials. Nevertheless, when it comes to the study of the scattering properties of finite-sized structures, dealing with the correct boundary conditions at the macroscopicscale becomes challenging. In this paper, we show how finite-domain boundary value problems canbe set-up in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized traction when non-local effects areneglected.The case of a metamaterial slab of finite width is presented, its scattering properties are studied viaa semi-analytical solution of the relaxed micromorphic model and compared to numerical simulationsencoding all details of the selected microstructure. The reflection coefficient obtained via the twomethods is presented as a function of the frequency and of the direction of propagation of the incidentwave. We find excellent agreement for a large range of frequencies going from the long-wave limitto frequencies beyond the first band-gap and for angles of incidence ranging from normal to nearparallel incidence. The case of a semi-infinite metamaterial is also presented and is seen to be areliable measure of the average behavior of the finite metastructure. A tremendous gain in termsof computational time is obtained when using the relaxed micromorphic model for the study of theconsidered metastructure
Fluid conduits and shallow-reservoir structure defined by geoelectrical tomography at the Nirano Salse (Italy)
Mud volcanoes are fluid escape structures allowing for surface venting of hydrocarbons (mostly gas but also liquid condensates and oils) and water–sediment slurries. For a better understanding of mud volcano dynamics, the characterization of the fluid dynamics within mud volcano conduits; the presence, extent, and depth of the fluid reservoirs; and the connection among aquifers, conduits, and mud reservoirs play a key role. To this aim, we performed a geoelectricalsurvey in the Nirano Salse Regional Nature Reserve, located at the edge of the northern Apennines (Fiorano Modenese, Italy), an area characterized by several active mud fluid vents. This study, for the first time, images the resistivity structure of the subsoil along two perpendicular cross sections down to a depth of 250 m. The electrical models show a clear difference between the northern and southern sectors of the area, where the latter hosts the main discontinuities. Shallow reservoirs, where fluid muds accumulate, are spatially associated with the main fault/fracture controlling the migration routes associated with surface venting and converge at depth towards a common clayey horizon. There is no evidence of a shallow mud caldera below the Nirano area. These findings represent a step forward in the comprehension of the Nirano Salse plumbing system and in pinpointing local site hazards, which promotes safer tourist access to the area along restricted routes
Scattering from a non-linear structured interface
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured interface modelled as elastica. In the first instance, the interaction between the masses is linearised. This allows for the study of a time-harmonic transmission model problem in the subcritical regime. Subsequently, we consider the transient problem associated with a non-linear ineraction within the interface. The effect of non-linearity is shown to suppress the transmission resonance observed in the linearised formulation
Nested Bloch waves in elastic structures with configurational forces
Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency