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声学超材料。例如，这些是声学有效的泡沫材料，其中局部共振效应将通过额外引入具有高刚性的固体来产生。这样就可以使这些材料的绝缘或阻尼效果得到显著改善，特别是在低频范围内。然而，到目前为止，对于如何设计声学超材料以达到最佳效果，特别是宽带效果，还没有一般的指导方针。因此，本课题旨在开发一种模拟方法，用于进一步研究声学超材料的机理、影响因素和设计参数以及拓扑优化。对于振动声分析，将发展有限单元法和边界元法的耦合。FCM将用于结构动力学计算，以充分有效地考虑超材料的非均质结构。为了评价不同的声超材料，使用了周围风量产生的声压和辐射声功率。声发射的计算是在边界元法的帮助下进行的，因为这是计算声场的有效可能性，特别是与体积离散方法相比，在远场进行评估。作为项目的一部分，高阶形状功能的好处也将被利用。在成功实施后，基于fe的商业计算程序、分析参考解决方案和实验调查将用于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.