Nonstandard continualization of 1D lattice with next-nearest interactions. Low order ODEs and enhanced prediction of the dispersive behavior

Gómez-Silva, F.; Fernández-Sáez, J.; Zaera, R.

doi:10.1080/15376494.2020.1799271

Cited by 17 publications

(4 citation statements)

References 34 publications

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“…Continualization methods deliver equivalent continua starting from a Lagrangian discrete system representation. Examples are the standard methods [68][69][70][71][72][73][74], the standard energy-based methods [70,72,[75][76][77][78], the improved and enhanced methods [73,74,[79][80][81][82][83][84] and the improved energy-based methods [85][86][87][88][89]. Along this research vein, in the theme issue, Del Toro et al [90] propose a high-frequency continualization scheme to study a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction.…”

Section: Modelling and Analysismentioning

confidence: 99%

Current developments in elastic and acoustic metamaterials science

Failla,

Marzani,

Palermo

et al. 2024

Phil. Trans. R. Soc. A.

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The concept of metamaterial recently emerged as a new frontier of scientific research, encompassing physics, materials science and engineering. In a broad sense, a metamaterial indicates an engineered material with exotic properties not found in nature, obtained by appropriate architecture either at macro-scale or at micro-/nano-scales. The architecture of metamaterials can be tailored to open unforeseen opportunities for mechanical and acoustic applications, as demonstrated by an impressive and increasing number of studies. Building on this knowledge, this theme issue aims to gather cutting-edge theoretical, computational and experimental studies on elastic and acoustic metamaterials, with the purpose of offering a wide perspective on recent achievements and future challenges. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1)’.

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Section: Modelling and Analysismentioning

confidence: 99%

Current developments in elastic and acoustic metamaterials science

Failla,

Marzani,

Palermo

et al. 2024

Phil. Trans. R. Soc. A.

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“…Among the homogenization schemes, we find asymptotic methods [26][27][28][29][30][31][32]; asymptotic variational methods [33][34][35]; and computational methods [36][37][38][39][40][41]. Among the continualization methods, we include the so-called standard methods [42][43][44][45][46][47][48][49], the standard energy-based methods [44,46,[50][51][52][53], the improved and enhanced methods [47,48,[54][55][56][57][58][59][60] and also the improved energy-based methods [61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

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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“…Polyzos and Fotiadis [34] employ several standard continualization procedures, leading to nonclassical continuum models with high-order differential equations, whereas Bacigalupo and Gambarotta [35] propose a non-standard continualization technique denominated Regularization, removing these high-order derivatives. Gómez-Silva et al [36] and Gómez-Silva and Zaera [37] [40] and Gómez-Silva and Zaera [41] study a lattice beam system considering bending deformation, Gómez-Silva and Zaera including next-nearest interactions in [42]. A modified semi-continuum Euler beam model with relaxation phenomenon is developed by Shen and Li in [43], where they present the bending deformation of a extreme-thin beam with micro/nano-scale thickness.…”

Section: Introductionmentioning

confidence: 99%