Homogenization of the vibro–acoustic transmission on periodically perforated elastic plates with arrays of resonators

Rohan, Eduard; Lukeš, Vladimír

doi:10.1016/j.apm.2022.05.040

Cited by 4 publications

(1 citation statement)

References 35 publications

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“…Let us also mention that such a homogenization process applied to acoustic reflection in a moving fluid on a non-planar surface has not been performed before, but there are some related studies on flow-coupled acoustics in the context of the homogenization. The problem of acoustic waves influenced by the advection velocity field has been treated in a bulk porous rigid and in deformable media [31], or in a layer containing a perforated plate [32], with particular examples using a potential flow model. Moreover, the transfer of incident waves into surface waves has been discussed in [33,34], characterizing in particular the influence of the shape of the plate perforations.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of thin-structured surfaces for acoustics in the presence of a two-dimensional low Mach potential flow

Mercier

2023

Proc. R. Soc. A.

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A surface homogenization method for acoustic waves over thin microstructured surfaces in the presence of a fluid in a potential flow is presented. Sound hard surfaces are considered, the flow is considered two-dimensional and slow and a low Mach approximation is introduced. We consider acoustic waves with a typical wavelength 1 / k much larger than the array spacing h and thickness e . Owing to the small parameter ε = k h , with e / h = O ( 1 ) , a matched asymptotic expansion technique is applied to the low Mach potential wave equation in the frequency domain. A boundary condition is obtained on an equivalent flat wall, which links the acoustic velocity to its normal and tangential derivatives (of the Myers type). The accuracy of the effective model is tested numerically for various periodic shapes and the accuracy of the model in O ( ε 2 ) is validated.

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Section: Introductionmentioning

confidence: 99%

Homogenization of thin-structured surfaces for acoustics in the presence of a two-dimensional low Mach potential flow

Mercier

2023

Proc. R. Soc. A.

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Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Lenders,

Liu,

Kouznetsova

2024

Comput Mech

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This paper introduces a computational homogenization framework for metamaterial plates consisting of locally resonant acoustic metamaterial (LRAM) unit cells. Based on the linearity assumption, the unit cell model is simplified through the superposition of long-wavelength (quasi-static) and local resonant eigenmode solutions. This method results in closed-form expressions describing the macroscale thin plate (shell) with enriched internal variable fields representing the amplitudes of the local resonant eigenmodes. The homogenized macroscopic shell model is implemented using isogeometric analysis, allowing for a straightforward handling of higher-order continuity requirements. Validation against fully-resolved direct numerical simulations (DNS) is conducted, showcasing the capability of the approach in computing the dispersion spectrum of an infinite LRAM plate, as well as performing frequency and time domain analyses of a finite LRAM plate. Results demonstrate that the homogenized enriched plate model accurately predicts wave attenuation within the frequency band-gaps, vibration modes, and wave propagation outside the band-gaps, achieving significantly reduced computational cost compared to DNS. The developed homogenization framework serves as a valuable computational tool for the analysis and design of LRAM panels of finite sizes and arbitrary shape under non-trivial excitations.

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Optimization of vibration and sound insulation in GPLRC honeycomb structures based on circle chaos mapping and Levy flight-enhanced YDSE with constraints

Yuan,

Liao,

Yuan

2024

Applied Mathematical Modelling

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Homogenization of the vibro–acoustic transmission on periodically perforated elastic plates with arrays of resonators

Cited by 4 publications

References 35 publications

Homogenization of thin-structured surfaces for acoustics in the presence of a two-dimensional low Mach potential flow

Homogenization of thin-structured surfaces for acoustics in the presence of a two-dimensional low Mach potential flow

Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Optimization of vibration and sound insulation in GPLRC honeycomb structures based on circle chaos mapping and Levy flight-enhanced YDSE with constraints

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