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Optimal layout design of porous media with and without base structure vibration in mid- to high-frequency structural–acoustic systems.

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Title: Optimal layout design of porous media with and without base structure vibration in mid- to high-frequency structural–acoustic systems.
Authors: Yu, Yang1,2 (AUTHOR) yuyang_1991131@163.com, Huang, Yutao1 (AUTHOR), Xu, Hengbo1 (AUTHOR), Li, Yonghua1,2 (AUTHOR), Chen, Bingzhi1,2 (AUTHOR), Zhao, Guozhong3 (AUTHOR)
Source: Structural & Multidisciplinary Optimization. Oct2025, Vol. 68 Issue 10, p1-25. 25p.
Subjects: Porous materials, Structural acoustics, Noise control, Energy transfer, Physical acoustics, Structural optimization, Energy dissipation
Abstract: This study introduces a layout optimization method for porous media aimed at minimizing noise in mid- to high-frequency structural–acoustic systems. In modal energy analysis, a power balance equation between uncoupled subsystems is proposed at a pure tone. Current methodologies for the topology optimization of porous media consider only the improvement in their acoustic properties, neglecting coupling with the base structure. In this study, porous media with and without base structure vibrations are considered, and an asymptotic approximation strategy is employed to estimate the modal damping loss factor, which is a critical parameter for measuring power dissipation in the power balance equation. In this layout optimization model, the design domain for porous media comprises a group of elements rather than single elements, with the corresponding material consumption designated as a constraint. To ensure that the design variable converges to a solution of 0 or 1, a hyperbolic tangent function is integrated into the solid isotropic material with a penalization scheme to form a dual penalization model. A gradient-based algorithm is used to solve the layout optimization problem, where the sensitivity is calculated via a combination of analytical derivation and a novel numerical differential technique insensitive to perturbation steps, namely, the complex variable method. The application of the asymptotic approximation strategy ensures that all modal information is computed within real mathematics and further ensures the feasibility of using the complex variable method. The effectiveness of the proposed method is demonstrated through a vibration transmission case and a sound transmission case. The optimization results reveal a significant reduction in the acoustic energy in mid- to high-frequency ranges for the different cases. Additionally, some interesting phenomena are observed, such as the narrowing of the gap among the modal acoustic energies and the increase in dispersion of the optimal porous media layouts as the frequency increases. [ABSTRACT FROM AUTHOR]
Copyright of Structural & Multidisciplinary Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Optimal layout design of porous media with and without base structure vibration in mid- to high-frequency structural–acoustic systems.
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  Data: <searchLink fieldCode="AR" term="%22Yu%2C+Yang%22">Yu, Yang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> yuyang_1991131@163.com</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Yutao%22">Huang, Yutao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Hengbo%22">Xu, Hengbo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Yonghua%22">Li, Yonghua</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Bingzhi%22">Chen, Bingzhi</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhao%2C+Guozhong%22">Zhao, Guozhong</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Structural+%26+Multidisciplinary+Optimization%22">Structural & Multidisciplinary Optimization</searchLink>. Oct2025, Vol. 68 Issue 10, p1-25. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Porous+materials%22">Porous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+acoustics%22">Structural acoustics</searchLink><br /><searchLink fieldCode="DE" term="%22Noise+control%22">Noise control</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+transfer%22">Energy transfer</searchLink><br /><searchLink fieldCode="DE" term="%22Physical+acoustics%22">Physical acoustics</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study introduces a layout optimization method for porous media aimed at minimizing noise in mid- to high-frequency structural–acoustic systems. In modal energy analysis, a power balance equation between uncoupled subsystems is proposed at a pure tone. Current methodologies for the topology optimization of porous media consider only the improvement in their acoustic properties, neglecting coupling with the base structure. In this study, porous media with and without base structure vibrations are considered, and an asymptotic approximation strategy is employed to estimate the modal damping loss factor, which is a critical parameter for measuring power dissipation in the power balance equation. In this layout optimization model, the design domain for porous media comprises a group of elements rather than single elements, with the corresponding material consumption designated as a constraint. To ensure that the design variable converges to a solution of 0 or 1, a hyperbolic tangent function is integrated into the solid isotropic material with a penalization scheme to form a dual penalization model. A gradient-based algorithm is used to solve the layout optimization problem, where the sensitivity is calculated via a combination of analytical derivation and a novel numerical differential technique insensitive to perturbation steps, namely, the complex variable method. The application of the asymptotic approximation strategy ensures that all modal information is computed within real mathematics and further ensures the feasibility of using the complex variable method. The effectiveness of the proposed method is demonstrated through a vibration transmission case and a sound transmission case. The optimization results reveal a significant reduction in the acoustic energy in mid- to high-frequency ranges for the different cases. Additionally, some interesting phenomena are observed, such as the narrowing of the gap among the modal acoustic energies and the increase in dispersion of the optimal porous media layouts as the frequency increases. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Structural & Multidisciplinary Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00158-025-04106-8
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      – Code: eng
        Text: English
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        PageCount: 25
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    Subjects:
      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Structural acoustics
        Type: general
      – SubjectFull: Noise control
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      – SubjectFull: Energy transfer
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      – SubjectFull: Physical acoustics
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      – SubjectFull: Structural optimization
        Type: general
      – SubjectFull: Energy dissipation
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      – TitleFull: Optimal layout design of porous media with and without base structure vibration in mid- to high-frequency structural–acoustic systems.
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            NameFull: Yu, Yang
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            NameFull: Huang, Yutao
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            NameFull: Chen, Bingzhi
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            – D: 01
              M: 10
              Text: Oct2025
              Type: published
              Y: 2025
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