Abstract In this paper, a new layout optimization technique is integrated with a statistical modal energy distribution analysis (SmEdA) model to obtain the optimal layout of a porous sound-absorbing material for noise control in mid-frequency vibro-acoustic systems. The considered optimization problem is minimizing the total energy of the internal acoustic cavity within the prescribed frequency range by reasonably positioning porous sound-absorbing material patches under a given volume constraint. The principle of SmEdA is based on the power balance between different modes of coupled structural and acoustic subsystems. A modal strain and kinetic energy (MSKE) method is employed to estimate the acoustic modal damping loss factors that are associated with the energy attenuation between different modes of the coupled subsystems. The developed real-valued optimization formulation provides the feasibility of adopting an accurate sensitivity analysis technique, the complex variable method (CVM). The effectiveness of the optimization procedure is demonstrated through a significant reduction in the total acoustic energy. Additionally, some conclusions with realistic significance are obtained: (a) The optimal material layout creates a more uniform distribution of modal energies in the SmEdA model; (b) The acoustic modes tend to move out of the prescribed frequency band through optimization.

中文翻译：

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中频振声系统中多孔吸声材料的布局优化

摘要 在本文中，一种新的布局优化技术与统计模态能量分布分析（SmEdA）模型相结合，以获得用于中频振动声系统噪声控制的多孔吸声材料的优化布局。考虑的优化问题是通过在给定的体积约束下合理定位多孔吸声材料贴片，在规定的频率范围内最小化内部声腔的总能量。SmEdA 的原理基于耦合结构和声学子系统的不同模式之间的功率平衡。采用模态应变和动能 (MSKE) 方法来估计与耦合子系统不同模态之间的能量衰减相关的声模态阻尼损耗因子。开发的实值优化公式提供了采用精确灵敏度分析技术，即复变量法 (CVM) 的可行性。优化程序的有效性通过总声能的显着减少来证明。此外，还获得了一些具有现实意义的结论： (a) 最佳材料布局在 SmEdA 模型中创建了更均匀的模态能量分布；(b) 通过优化，声学模式往往会移出规定的频带。得到了一些具有现实意义的结论： (a) 最佳材料布局在 SmEdA 模型中创造了更均匀的模态能量分布；(b) 通过优化，声学模式往往会移出规定的频带。得到了一些具有现实意义的结论： (a) 最佳材料布局在 SmEdA 模型中创造了更均匀的模态能量分布；(b) 通过优化，声学模式往往会移出规定的频带。