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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Yang Yu,
  • Yutao Huang,
  • Hengbo Xu,
  • Yonghua Li,
  • Bingzhi Chen,
  • Guozhong Zhao

摘要

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.