Multifield nested metafilters for wave propagation control

Fantoni, Francesca; Bosco, E.; Bacigalupo, Andrea

doi:10.1016/j.eml.2022.101885

Cited by 9 publications

(6 citation statements)

References 91 publications

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“…denote the invariants concerning the longitudinal (ψ = L) and transverse waves (ψ = T). According to the methodology exposed in Fantoni et al [70], the limit values of the invariants I 1 ψ , related to the identification of pass bands, fall within −2 ≤ I 1 ψ ≤ 2.…”

Section: (A) Bloch Wave Propagationmentioning

confidence: 99%

“…In such a case, they lie out of the unit circle by indicating the presence of a stop band. The spectral effects of transverse elastic waves can be analysed by establishing the transmission coefficient, denoted as c t = − 20log [70,82,83]. This study is illustrated in figure 3 that focuses on the transverse displacement with respect to the dimensionless angular frequency for the cases of S 2 = BAA in figure 3a, 3b and S 4 = BAABBBAABAA in figure 3c by growing up the number of generations as one (red curves), 40 (green curves) and 50 (orange curves), with fixed parameters r C = r ρ = 2 and η = 1.…”

Section: Representative Examplesmentioning

confidence: 99%

“…According to the methodology exposed in Fantoni et al . [70], the limit values of the invariants true0 mathcalscriptI 1 ( ψ ) , related to the identification of pass bands, fall within true0 − 2 ≤ mathcalscriptI 1 ( ψ ) ≤ 2 . Stop bands can be identified for values of true0 mathcalscriptI 1 ( ψ ) beyond this range.…”

Section: Mechanics Of Fibonacci Superlatticesmentioning

confidence: 99%

“…This elementary cell, named also as Fibonacci generation, is made of two homogeneous elastic building blocks (layers) organized according to the generalized Fibonacci sequence. The propagation of Bloch waves in periodic approximants representative of Fibonacci superlattices is studied through the effective transfer matrix method [66][67][68][69][70][71]. More specifically, by exploiting the Floquet-Bloch decomposition the symplectic transfer matrix of the Fibonacci generation is determined in closed-form in turn.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic continualization of mechanical metamaterials with quasi-periodic microstructure

Del Toro,

De Bellis,

Bacigalupo

2024

Phil. Trans. R. Soc. A.

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This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet–Bloch theory to validate the proposed scheme. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1).’

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Section: (A) Bloch Wave Propagationmentioning

confidence: 99%

Section: Representative Examplesmentioning

confidence: 99%

Section: Mechanics Of Fibonacci Superlatticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic continualization of mechanical metamaterials with quasi-periodic microstructure

Del Toro,

De Bellis,

Bacigalupo

2024

Phil. Trans. R. Soc. A.

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“…More specifically, for each dimensionless angular frequency and for a given complex multiplier , with , the eigenvalue , with and , as well as the eigenvector (for , where M is the eigen-problem dimension) are determined. Then, the frequency spectrum is finally determined exploiting the mapping 32 – 39 . Based on the obtained frequency spectra, the relative band gap between the h -th and q -th (consecutive) dispersion functions with can be evaluated by solving the -parametrized generalized eigen-problem in ( 1 ) as …”

Section: Dispersion Properties For Elastic Periodic Metafiltersmentioning

confidence: 99%

On dispersion curve coloring for mechanical metafilters

Bacigalupo

Bellis

Gnecco

et al. 2022

Sci Rep

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This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, written as functions of a scalar parameter. The algorithm is based on a first-order finite difference approximation of the curves and a sequence of prediction/correction steps. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving an Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming technique is presented. The proposed algorithm is applied with success to elastic periodic metamaterials for the realization of high-performance mechanical metafilters. Its output is shown to be in excellent agreement with desirable smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out.

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