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Giorgio Carta's blog

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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.

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Transmission and localisation in ordered and randomly-perturbed structured flexural systems

The paper presents a novel analysis of localisation and transmission properties of randomly-perturbed flexural systems. Attention is given to the study of propagation regimes and the connection with localised resonance modes in the context of Anderson's localisation. The analytical study is complemented with numerical simulations relevant to the design of efficient vibration isolation systems.


Eigenvalues, reflected and transmitted energy, localisation factors for the examined bi-coupled random system:

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Continuous and discrete microstructured materials with null Poisson's ratio

In this paper we propose different classes of isotropic microstructured media with tunable Poisson's ratio. The elastic periodic systems are continuous porous media and two- and three-dimensional lattices. The microstructural parameters can be tuned in order to have an effective Poisson's ratio equal to zero. The connection between microstructural parameters and effective properties is shown in detail both analytically and numerically.


Continuous system with null Poisson's ratio:

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Design of a porous material with isotropic negative Poisson's ratio

This paper proposes the design of a two-dimensional porous solid with omnidirectional negative Poisson's ratio. The hexagonal periodic distribution of the pores makes the effective behavior isotropic. Both experimental tests and numerical simulations have been performed to determine the effective properties of the porous solid. A parametric study on the effect of the geometrical microstructural parameters is also presented. This auxetic structure is easy to fabricate and can be very useful in several engineering applications.


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Bloch-Floquet waves in flexural systems with continuous and discrete elements

In this paper we describe the dynamic behavior of elongated multi-structured media excited by flexural harmonic waves. We examine periodic structures consisting of continuous beams and discrete resonators disposed in various arrangements. The transfer matrix approach and Bloch-Floquet conditions are implemented for the determination of different propagation and non-propagation regimes.

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Dynamic response and localisation in strongly damaged waveguides

In this paper, we investigate the formation of band-gaps and localisation phenomena in an elastic strip nearly disintegrated by an array of transverse cracks. We analyse the eigenfrequencies of finite, strongly damaged, elongated solids with reference to the propagation bands of an infinite strip with a periodic damage. Subsequently, we determine analytically the band-gaps of the infinite strip by using a lower-dimensional model, represented by a periodically-damaged beam in which the small ligaments between cracks are modelled as ‘elastic junctions’.

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Dispersion properties of vortex-type monatomic lattices

The paper presents a systematic study of dispersive waves in an elastic chiral lattice. Chirality is introduced through gyroscopes embedded into the junctions of a doubly periodic lattice. Bloch-Floquet waves are assumed to satisfy the quasi-periodicity conditions on the elementary cell.

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Temperature induced crack propagation in structured media

This paper describes the propagation of an edge crack in a semi-infinite triangular lattice, consisting of identical point masses connected by thermoelastic links. A change of temperature, represented by a time-periodic series of high-gradient temperature pulses, is applied at the boundary of the lattice. In order to make the initial crack advance in the lattice a failure criterion is imposed, whereby the links break as soon as they attain a prescribed elongation.

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