Coupling of fictitious domain methods and the boundary element method for the analysis of acoustic metamaterials

本项目提案的重点是创新的声学超材料。例如，这些是声学有效的泡沫材料，其中通过额外引入具有高刚性的固体来产生局部共振效应。这样，这些材料的隔音或减振效果应该会得到显著改善，特别是在低频范围内。然而，到目前为止，如何设计声学超材料以达到最好的效果，特别是宽带效果，目前还没有通用的指导原则。为此，本项目旨在开发一种仿真方法，用于对声学超材料的机理、影响因素和设计参数进行广泛的分析，并在进一步研究中用于声学超材料的拓扑优化。对于振动声学分析，将发展有限单元法(FCM)和边界元方法(BEM)的耦合。FCM将用于结构动力学计算，以充分和有效地考虑超材料的非均质结构。为了评估不同的声学超材料，使用了周围空气中产生的声压以及辐射声功率。声发射的计算是在边界元的帮助下进行的，因为与体积离散化方法相比，这是计算声场的一种有效的可能性，特别是对于远场的评估。作为该项目的一部分，还将利用高阶形状函数的好处。在成功实施后，将使用基于商业有限元的计算程序、分析参考解和实验研究来验证和验证所开发的方法。

This project proposal focuses on innovative acoustic metamaterials. These are, for example, acoustically effective foam materials in which local resonance effects are to be produced by additionally introduced solids with high rigidity. In this way it should be achieved that the insulating or damping effect of these materials is significantly improved, especially in the low-frequency range.However, so far there are no general guidelines on how to design an acoustic metamaterial in order to achieve the best possible and in particular a broadband effect. For this reason, the proposed project aims to develop a simulation methodology, which can be used for an extensive analysis of the mechanisms, influencing factors and design parameters as well as the topology optimization of acoustic metamaterials in further studies. For the vibroacoustic analysis a coupling of the Finite Cell Method (FCM) and the boundary element method (BEM) will be developed. The FCM will be used for structural dynamics calculations to consider the heterogeneous structure of the metamaterials adequately and efficiently. For the evaluation of different acoustic metamaterials, the resulting sound pressure in the surrounding air volume as well as the radiated sound power is used. The calculation of the sound emission takes place with the aid of the BEM, since this is an efficient possibility for the calculation of the acoustic field, in particular for the evaluation in the far field in comparison to volume discretizing methods. As part of the project, the benefits of high-order shape functions will also be exploited. After successful implementation, commercial FE-based calculation programs, analytical reference solutions and experimental investigations will be used to verify and validate the developed methods.