Abstract This paper aims at consolidating research dealing with vibroacoustics of periodic media. The main goal of this work is to develop and to validate tools for the design of global vibroacoustic treatments based on periodic patterns, allowing passive control of acoustic paths in layered concepts. To this aim, some enhancements are introduced to the state of the art on the study and the design of Biot-modeled foams, in order to obtain desired acoustics performances through embedded periodic inclusions. At first, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, is introduced. Successively, through the use of the acoustic-structure coupling that comes from the implementation of Biot model, a non-rigid inclusion test campaign is carried out by considering some solid (but still non-perfectly-rigid) inclusions in a 3D-modeled unit cell; in particular, six setups are discussed herein. Then, some design guidelines are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of unit cell dimensions, airflow resistivity, tortuosity, viscous and thermal characteristic lengths, frame density, Young modulus and loss factor; conversely, it is shown also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency.

中文翻译：

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周期性 Biot 模型泡沫的声学特性计算和设计指南

摘要 本文旨在巩固有关周期介质振动声学的研究。这项工作的主要目标是开发和验证基于周期性模式的全局振动声处理设计工具，允许在分层概念中被动控制声学路径。为此，对 Biot 模型泡沫的研究和设计的最新技术进行了一些改进，以便通过嵌入的周期性夹杂物获得所需的声学性能。首先，介绍了所研究的由多孔弹性 3D 晶胞构成的声学包的特性。随后，通过使用来自 Biot 模型实现的声学-结构耦合，非刚性夹杂物测试活动是通过考虑 3D 建模单元中的一些固体（但仍然不是完全刚性的）夹杂物来进行的；特别地，这里讨论了六种设置。然后，提供了一些设计指南，以预测第一个性能峰值出现的频率及其幅度，作为晶胞尺寸、气流电阻率、弯曲度、粘性和热特征长度、框架密度、杨氏模量和损耗的函数因素; 相反，它还显示了晶胞尺寸与作为设计频率函数的第一性能峰值幅度之间的联系。连同其振幅，作为晶胞尺寸、气流电阻率、弯曲度、粘性和热特征长度、框架密度、杨氏模量和损耗因子的函数；相反，它还显示了晶胞尺寸与作为设计频率函数的第一性能峰值幅度之间的联系。连同其振幅，作为晶胞尺寸、气流阻力、弯曲度、粘性和热特征长度、框架密度、杨氏模量和损耗因子的函数；相反，它还显示了晶胞尺寸与作为设计频率函数的第一性能峰值幅度之间的联系。