Extended acoustic waves in diluted random systems

Costa, A. E. B.; Moura, F. A. B. F. de

doi:10.1140/epjb/e2011-20016-3

Cited by 9 publications

(6 citation statements)

References 44 publications

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“…Correlated disorder has also been investigated in long range spring-mass chain for DNA modelling 17 and extended acoustic waves. 18 In addition, it has been known for decades this kind of near-periodicity can be designed for enhanced vibroacoustic attenuation performance. 19–22 Similarly, randomness and break of periodicity can also be used to modify the performance of metastructures.…”

Section: Introductionmentioning

confidence: 99%

Correlated disorder in rainbow metamaterials for vibration attenuation

Fabro

Meng

Chronopoulos

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Metastructures are typically composed of periodic unit cells designed to present enhanced dynamic properties in which either single or multiple resonators are periodically distributed. Even though the periodic metamaterials can obtain bandgaps with outstanding vibration attenuation, the widths of bandgaps can still be narrow for some practical applications. Rainbow metamaterials have been proposed based on gradient or random profiles to provide further improved attenuation. Nonetheless, the effects of correlated random disorder on their attenuation performance remains an open challenge. This work presents an investigation on the effects of correlated disorder on the vibration attenuation of rainbow metamaterials. An analytical model using the transfer matrix approach is used to calculate the receptance functions in a finite length metastructure composed of evenly spaced non-symmetric resonators attached to a beam with Π-shaped cross-section, thus a multi-frequency metastructure. The correlated disorder is modelled using random fields and an analytical expression of the Karhunen-Loève expansion is used such that spatial correlation on the resonator properties is modified by various correlation lengths, i.e., the level of spatial smoothness. Individual samples of random fields are used to investigate the effects of the correlated disorder in the vibration attenuation of a multi-frequency metastructure. It is shown that the bandgap can be further widened when compared to uncorrelated disorder. The obtained results indicates that a combination of the gradient profile with some level of disorder, typically resulting from random fields with larger correlation lengths, tends to give improved vibration attenuation when compared to a optimized gradient rainbow metamaterial. It opens new and innovative ways for the design of broadband rainbow metastructures for vibration attenuation.

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Section: Introductionmentioning

confidence: 99%

Correlated disorder in rainbow metamaterials for vibration attenuation

Fabro

Meng

Chronopoulos

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Currently, Anderson localization transition is well-understood in one-dimensional (1D) random media [1][2][3][4][5]. According to the scaling theory of localization [1], in 1D systems, any weak white noise disorder will localize all the (electron) states [6].…”

Section: Introductionmentioning

confidence: 99%

“…They numerically showed that for a binary chain exhibiting long-range correlations (LRC) with a scaling exponent α greater than a threshold value (α c ∼ 1.45), there is a broad energy band of extended (delocalized) states. Alternatively, the extended states can be produced by the presence of short-range correlations (SRC) in binary random sequences [4,14,15], e.g., the random-dimer model [5,16]. Consequently, short-and long-range correlations are used to examine the localization-delocalization transition in disordered chains [4,5,8,14,16].…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, the extended states can be produced by the presence of short-range correlations (SRC) in binary random sequences [4,14,15], e.g., the random-dimer model [5,16]. Consequently, short-and long-range correlations are used to examine the localization-delocalization transition in disordered chains [4,5,8,14,16]. Also, heat conduction in 1D harmonic chains with correlated disorder has long been a subject of investigation [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Entropic analysis of the localization–delocalization transition in a one-dimensional correlated lattice

Farzadian

Oikonomou

Good

et al. 2020

Physica A: Statistical Mechanics and its Applications

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In this work, propagation of acoustic waves in a one-dimensional binary chain with different types of correlations in elasticity distribution is studied. We applied entropic analysis to investigate and quantify the localization-delocalization transition in long-range correlated chains in terms of the scaling exponent α and discuss its relation to the order-disorder levels in the structure of the chain. The results demonstrated that the entropic consideration detects correctly the critical value of α separating localization from delocalization bands. * Electronic address: thomas.oikonomou@nu.edu.kz

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“…The formalism of the localization theory applies also to the study of magnon localization in random ferromagnets [18,19], collective vibrational motion of one-dimensional (1D) disordered harmonic chains [20][21][22] and acoustic waves in disordered media [23][24][25][26][27][28][29][30][31][32][33][34][35]. In fact, the propagation of acoustic waves has attracted both theoretical [23][24][25][26][27][28][29][30][31][33][34][35] and experimental [32] interest. Along general lines, it was shown that such waves may be localized in media with uncorrelated disorder.…”

Section: Introductionmentioning

confidence: 99%

Extended acoustic modes in random systems withn-mer short range correlations

Barros

Costa

Moura

2011

J. Phys.: Condens. Matter

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In this paper we study the propagation of acoustic waves in a one-dimensional medium with a short range correlated elasticity distribution. In order to generate local correlations we consider a disordered binary distribution in which the effective elastic constants can take on only two values, η(A) and η(B). We add an additional constraint that the η(A) values appear only in finite segments of length n. This is a generalization of the well-known random-dimer model. By using an analytical procedure we demonstrate that the system displays n - 1 resonances with frequencies ω(r). Furthermore, we apply a numerical transfer matrix formalism and a second-order finite-difference method to study in detail the waves that propagate in the chain. Our results indicate that all the modes with ω ≠ ω(r) decay and the medium transmits only the frequencies ω(r).

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Extended acoustic waves in diluted random systems

Cited by 9 publications

References 44 publications

Correlated disorder in rainbow metamaterials for vibration attenuation

Correlated disorder in rainbow metamaterials for vibration attenuation

Entropic analysis of the localization–delocalization transition in a one-dimensional correlated lattice

Extended acoustic modes in random systems withn-mer short range correlations

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