1,721,095 research outputs found
Scaling laws and ultra-wide band gaps in generalized Fibonacci structures: a new paradigm for the design of quasicrystalline waveguides
No full textWave propagation in one-dimensional quasicrystalline structures: dynamical trace mapping and self-similar stop/pass band distribution
No full textOne-dimensional quasiperiodic and quasicrystalline structures: dynamic spectra and self-similar pattern identification
No full textMathematical theory for supercell approximations of fibonacci quasicrystals
No full textWe present mathematical theory showing that supercell approximations accurately predict the main spectral gaps of Fibonacci quasicrystals. This theory is based on characterising the growth of the underlying recursion relation and corroborates the existence of previously observed “super band gaps”. We demonstrate our general theory through application to a one-dimensional metamaterial, composed of a system of structured rods
Quasiperiodic modulated structures: stop/pass band distribution and self-similar pattern identification
No full textElastic waves in two-phase composite quasicrystalline-generated metamaterials: scaling of frequency spectra and negative refraction
Full text linkWaves in one-dimensional quasicrystalline structures: dynamical trace mapping, scaling and self-similarity of the spectrum
No full textHarmonic axial waves in quasiperiodic-generated structured rods are investigated. The focus is on infinite bars composed of repeated elementary cells designed by adopting generalised Fibonacci substitution rules, some of which represent examples of one-dimensional quasicrystals. Their dispersive features and stop/pass band spectra are computed and analysed by imposing Floquet–Bloch conditions and exploiting the invariance properties of the trace of the relevant transfer matrices. We show that for a family of generalised Fibonacci substitution rules, corresponding to the so-called precious means, an invariant function of the circular frequency, the Kohmoto's invariant, governs self-similarity and scaling of the stop/pass band layout within defined ranges of frequencies at increasing generation index. Other parts of the spectrum are instead occupied by almost constant ultrawide band gaps. The Kohmoto's invariant also explains the existence of particular frequencies, named canonical frequencies, associated with closed orbits on the geometrical three-dimensional representation of the invariant. The developed theory represents an important advancement towards the realisation of elastic quasicrystalline metamaterials
Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials
No full textAn original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight function matrices are used together with a generalized Betti's reciprocity theorem in order to derive a system of integral equations that relate the applied loading, the temperature and mass concentration fields, the heat and mass fluxes on the fracture surfaces and the resulting crack opening. The obtained integral identities can have many relevant applications, such as for the modelling of crack and damage processes at the interface between different components in electrochemical energy devices characterized by multi-layered structures (solid oxide fuel cells and lithium ions batteries)
Negative refraction for anti-plane elastic waves in canonical quasicrystalline laminates
Full text linkElastic anti-plane shear waves can be refracted negatively when they are transmitted across an interface between a homogeneous substrate and a transverse periodic laminate. To achieve pure negative refraction, the frequency of the source should be lower than the upper limit of the second transition zone of the harmonic spectrum of the laminate. An effective way to control the location of transition zones is to consider a canonical configuration for the laminate, a concept that originates from the properties of quasicrystalline sequences among which the Fibonacci one is a particular case. We give a detailed account of the classification in three families of canonical configurations and the role of canonical frequency. We exploit the knowledge of the scaling factor of the self-similar structure of the layout of transition zones for laminates of this kind to provide a quantitative tool to predict the relevant frequencies to accomplish negative refraction. We also investigate how the change of other parameters of the elementary cell may affect the values of those frequencies. The obtained results show that the features of quasicrystalline sequences may be profitably exploited for the realisation of elastic metamaterials
Design of interface modes in canonical phononic waveguides
No full textAn interface mode is a localised vibration field at the interface between two waveguides that may be excited at a frequency sitting in a band gap that is in common between the two structures. For electromagnetic waves, the condition for the mode to occur is associated with certain properties of either the surface impedances of the two waveguides or the value of the Zak phase of the adjacent pass bands. In this work, we propose a novel, rigorous and simple method to predict the presence of interface modes at the join between two dissimilar, one-dimensional, periodic, two-phase phononic waveguides. In particular, we show that when the two rods have a canonical configuration it is possible to determine the band gaps of the frequency spectrum where this condition is satisfied. The value of the impedance for all band gaps of the spectrum is analysed through an extended version of the method of the universal toroidal manifold, recently adopted by the Authors to describe the dynamic properties of canonical structures. In terms of prediction, the outcome of the proposed approach is identical to that derived by calculating the Zak phase of the bulk bands for both the waveguides composing the system. By considering two specific combinations of finite-sized canonical rods and studying the associated reflection coefficients, we also determine the frequency of the interface mode in closed form. Our approach provides significant new insight to the mechanics of structured waveguides in order to design and optimise systems able to support interface modes avoiding the challenging numerical calculations normally required to estimate topological invariants
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