arXiv subjects

Giorgio Carta

Publications and source records attributed to Giorgio Carta.

7 recordsLinked to original sources

arXiv2026

Predictive beam-lattice reduction for higher-order topological modes in a 2D SSH phononic crystal

We develop a mechanically faithful reduced model for a two-dimensional topological phononic crystal composed of rigid square masses connected by slender elastic ligaments. Exploiting Euler Bernoulli beam theory, we derive a Hermitian 12 degree of freedom dynamical matrix that retains in-plane translations, rotations, and ligament eccentricity. This reduction captures effects that are absent from scalar mass spring SSH models while remaining computationally much more tractable and more easily interpretable than full finite element simulations. Dimerizing the ligament widths produces a mechanical 2D SSH lattice with a full band gap and a quantized bulk polarization. The sign of the dimerization controls the transition from trivial to non trivial phases, while ligament eccentricity provides an additional purely geometric mechanism for changing the topology. Ribbon and finite cell calculations predict in gap edge and corner modes, quantified by localization measures and confirmed by finite element simulations. Measurements on 3D printed samples show an evanescent response in the trivial structure and enhanced boundary/corner response in the non trivial structure within the predicted gap. The results provide a validated route for designing topological elastic metamaterials using a continuum informed discrete model rather than either idealized mass spring networks or brute force numerical optimization.

physics.comp-ph↗

arXiv2023

The strange case of Negative Reflection

In this paper we show for the first time the phenomenon of negative reflection in a simple mechanical structure. The latter is a grating of fixed inclusions embedded in a linear elastic matrix. Numerical analyses for out-of-plane shear waves demonstrate that there exist frequencies at which most of the incident energy is reflected at negative angles. The effect is symmetric with respect to a line that is not parallel to the normal direction to the grating structure. Simulations at different angles of incidence and computations of the energy fluxes show that negative reflection is achievable in a wide range of loading conditions.

physics.class-ph↗

arXiv2022

Hierarchical auxetic and isotropic porous medium with extremely negative Poisson's ratio

We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes the medium isotropic in the plane. Remarkably, the mesoscale interaction between the first- and second-level cuts enables the attainment of a value of the Poisson's ratio close to the minimum reachable limit of -1. The effective properties of the hierarchical auxetic structure are determined numerically, considering both a unit cell with periodic boundary conditions and a finite structure containing a large number of repeating cells. Further, results of the numerical study are validated experimentally on a polymeric specimen with appropriately arranged rank-two cuts, tested under uniaxial tension. We envisage that the proposed hierarchical design can be useful in numerous engineering applications exploiting an extreme auxetic effect

physics.app-ph↗

arXiv2018

Vibrations and elastic waves in chiral multi-structures

We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundary conditions describing the interaction between an elastic beam and a gyroscopic spinner. These conditions are applied to the analysis of waves in systems of beams connected by gyroscopic spinners. A new asymptotic and physical interpretation of the notion of a Rayleigh gyrobeam is also presented. The theoretical findings are accompanied by illustrative numerical examples and simulations.

physics.class-ph↗

arXiv2018

Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems

This paper presents a mathematical model for an industry-inspired problem of vibration isolation applied to elastic fluid-filled containers. A fundamental problem of suppression of vibrations within a finite-width frequency interval for a multi-scale fluid-solid system has been solved. We have developed a systematic approach employing full fluid-solid interaction and dispersion analysis, which can be applied to finite and periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and transient regime computations.

physics.flu-dyn↗

arXiv2018

Interfacial waveforms in chiral lattices with gyroscopic spinners

We demonstrate a new method of achieving topologically protected states in a discrete hexagonal lattice by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail and, by tuning the parameters of the spinners, it is shown one can manipulate the locations of stop-bands and Dirac points. We show that in proximity of such points, uni-directional interfacial waveforms can be created in an inhomogeneous lattice and the direction of such waveforms can be controlled. The effect of inserting additional internal links into the system, which is thus transformed in a heterogeneous triangular lattice, is also investigated. This work introduces a new perspective in the design of periodic media possessing non-trivial topological features.

physics.class-ph↗

arXiv2015

Porous Materials with Omnidirectional Negative Poisson's Ratio

This paper presents an auxetic medium, consisting of a two-dimensional perforated sheet where the holes are arranged in a repetitive pattern. The hexagonal disposition of the perforations makes the medium isotropic in the plane. It is shown that negative values of the Poisson's ratio can be achieved for specific values of the dimensions and orientations of the holes. The results of the numerical simulations are confirmed by experimental tests, in which the Poisson's ratio of each specimen examined is evaluated from the displacement field obtained from the Digital Image Correlation (DIC) technique. The distribution of stresses in the medium is determined directly from photoelastic images. The auxetic structure proposed in this paper is easy to fabricate and can be very useful in several engineering applications.

cond-mat.mtrl-sci↗