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<p>Uncertainties are widespread and unavoidable in engineering structures, and acoustic metamaterials are no exception. Up to now, one of the most common approaches to model these uncertainties is the interval model. In this paper, a novel interval finite element method is proposed to investigate the influences of these uncertainties on the band gap. Firstly, the interval dynamic equation of metamaterial structures is obtained based on commercial software Abaqus. Then, a response surface method is used to solve this interval dynamic equation, based on which an interval vibration transmission analysis can be easily carried out and the safe band gap can be defined. Finally, three numerical examples are presented to demonstrate the efficiency and accuracy of the response surface method. Results show that these uncertainties can even reduce the safe band gap range by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1664_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(20.21 \%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20.21</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, compared to the deterministic band gap range. This indicates that the uncertainty analysis of the metamaterial structures is actually very necessary.</p>

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Band Gap Properties of Acoustic Metamaterials with Interval Parameters

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Feiyang He,
  • Denghui Qian,
  • Zhiyu Shi,
  • Guo Wei

摘要

Uncertainties are widespread and unavoidable in engineering structures, and acoustic metamaterials are no exception. Up to now, one of the most common approaches to model these uncertainties is the interval model. In this paper, a novel interval finite element method is proposed to investigate the influences of these uncertainties on the band gap. Firstly, the interval dynamic equation of metamaterial structures is obtained based on commercial software Abaqus. Then, a response surface method is used to solve this interval dynamic equation, based on which an interval vibration transmission analysis can be easily carried out and the safe band gap can be defined. Finally, three numerical examples are presented to demonstrate the efficiency and accuracy of the response surface method. Results show that these uncertainties can even reduce the safe band gap range by \(20.21 \%\) 20.21 % , compared to the deterministic band gap range. This indicates that the uncertainty analysis of the metamaterial structures is actually very necessary.