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Analytical fractal model of sound absorption for cellular foams with randomly distributed fully/semi-open pores

具有随机分布的全/半开孔隙的多孔泡沫吸声分形模型

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Abstract

Cellular foams with randomly distributed open pores are increasingly exploited in sound management applications, where the sound absorption coefficient (SAC) typically serves as a crucial acoustic parameter for performance evaluation and design optimization. Dependent upon the processing method, the pores in a cellular foam can be either fully open or semi-open and often exhibit fractal distribution features. To facilitate engineering applications, it is imperative to analytically predict the SACs of these foams. However, predicting analytically the SAC for foams poses a challenge. Therefore, this study proposes a simplified representative structure (RS) with semi-open or fully open pores to analyze the flow properties within the foam microscopically, while the fractal theory is applied to portray the randomly distributed pores. With the extent to which the pores are open characterized using a purposely introduced parameter called the open-pore degree, both viscous and thermal characteristic lengths of the RS are analytically obtained. Subsequently, built upon the classical Johnson-Champoux-Allard (JCA) model for sound propagation in porous media, an analytical model is developed to unify the RS with the fractal theory so that the SAC can be predicted as a function of key morphological parameters of the foam having fully/semi-open pores. Compared with existing experimental measurements and numerical simulation results, the proposed analytical model predicts well the key flow properties as well as the SAC of foams having either semi-open or fully open pore topologies. In the frequency range of 0–4500 Hz, a semi-open foam can better attenuate the sound wave relative to its fully-open counterpart having the same porosity. With the porosity fixed at 0.95, the overall SAC of semi-open foam is improved by 21.2%, 57.7%, and 75.8%, respectively, as its open-pore degree is reduced from 0.75 via 0.50 to 0.25.

摘要

具有随机孔隙的多孔泡沫在声音管理应用中得到越来越多的利用, 其吸声系数通常作为性能评估和设计优化的关键声学参数. 根据不同的加工方法, 泡沫中的孔隙可以是全开或半开的, 并且通常表现为分形分布特征. 为了便于工程应用, 有必要对这些泡沫的吸声系数进行分析预测. 然而, 分析预测泡沫的吸声系数是一个挑战. 因此, 本研究提出了半开孔和全开孔的简化代表结构来微观分析泡沫内部的流动特性, 并应用分形理论来描述随机分布的孔隙. 引入一个叫“开孔度”的参数来表征孔隙的开放程度, 可以解析地获得代表结构的粘性和热特征长度. 随后, 在经典吸声系数Johnson-Champoux-Allard模型的基础上, 建立了一种将代表结构与分形理论统一起来的解析模型, 从而可以将吸声系数作为具有全开/半开孔泡沫的关键形态参数的函数进行预测. 与已有的实验测量和数值模拟结果相比, 本文提出的分析模型可以较好地预测了半开孔和全开孔泡沫的关键流动特性和吸声系数. 在0到4500 Hz的频率范围内, 半开孔泡沫相对于具有相同孔隙率的全开孔泡沫可以更好地衰减声波. 在孔隙率为0.95的条件下, 半开孔泡沫的总体吸声系数分别提高了21.2%、57.7%和75.8%, 此时开孔度由0.75到0.50降低了0.25.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51976155 and 12032010), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Grant No. MCMS-I-0222K01), and the Fund of Prospective Layout of Scientific Research for Nanjing University of Aeronautics and Astronautics. One of the authors (Xiaohu Yang) gratefully acknowledged the support of K. C. Wong Education Foundation.

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Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Tian Xiao  (肖田) & Chenlei Yu  (于晨磊)

  2. Institute of the Building Environment & Sustainability Technology, School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Liu Lu  (卢溜), Gao Shu  (舒高) & Xiaohu Yang  (杨肖虎)

  3. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Tian Jian Lu  (卢天健)

  4. MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures (MLMS), Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Tian Jian Lu  (卢天健)

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  1. Tian Xiao  (肖田)
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  2. Liu Lu  (卢溜)
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  3. Chenlei Yu  (于晨磊)
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  4. Gao Shu  (舒高)
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  5. Xiaohu Yang  (杨肖虎)
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  6. Tian Jian Lu  (卢天健)
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Contributions

Author contributions Tian Xiao and Xiaohu Yang designed the research. Tian Xiao wrote the first draft of the manuscript. Xiaohu Yang proposed the conceptualization. Tian Xiao and Xiaohu Yang developed models. Liu Lu, Chenlei Yu, and Gao Shu completed the data curation and analyzed study data. Liu Lu, Xiaohu Yang, and Tian Jian Lu helped organize the manuscript. Tian Xiao, Xiaohu Yang, and Tian Jian Lu revised and edited the final version.

Corresponding authors

Correspondence to Xiaohu Yang  (杨肖虎) or Tian Jian Lu  (卢天健).

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Conflict of interest On behalf of. all authors, the corresponding author states that there is no conflict of interest.

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Xiao, T., Lu, L., Yu, C. et al. Analytical fractal model of sound absorption for cellular foams with randomly distributed fully/semi-open pores. Acta Mech. Sin. 40, 423109 (2024). https://doi.org/10.1007/s10409-023-23109-x

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