Deliberate introduction of acoustic radiation damping using locally resonant materials

许多轻型结构都是刚性和弱阻尼的。这一观察结果也适用于许多乐器和一些水下结构。这些结构的共同点是声辐射阻尼可能与其他阻尼机制具有相似甚至更高的量级。本提案旨在研究此类情况，并提供数学公式，允许在纯结构模型中考虑声辐射阻尼，尽管实际物理需要耦合结构声学模型。然而，在数学上，结构声学模型可以简化为一个结构模型，其中舒尔补代表整个流体行为。本课题对声辐射阻尼进行了定量研究，旨在建立一个考虑声辐射阻尼而不解决声辐射问题的数学模型。除了实际的辐射阻尼外，定量估计还包括对声学边界元公式中出现的数值阻尼和可能与高频相关的流体阻尼的研究。非耦合结构模型可以将辐射阻尼视为模态阻尼或粘弹性层理。最后，将开发和研究利用声辐射阻尼的结构。

Many lightweight structures are stiff and weakly damped. This observation holds for a number of musical instruments and some submerged structures too. These structures have in common that acoustic radiation damping may be of a similar or even higher magnitude than other damping mechanisms. This proposal is directed to investigate such cases and to provide mathematical formulations which allow to consider acoustic radiation damping in a purely structural model although the actual physics would require a coupled structural acoustic model. However, mathematically, the structural acoustic model can be reduced to a structural one where the Schur complement represents the entire fluid behavior. This project investigates acoustic radiation damping quantitatively and aims at the development of a mathematical model to consider acoustic radiation damping without solution of the acoustic radiation problem. Beside the actual radiation damping, the quantitative estimation includes investigation of numerical damping occurring in acoustic BEM formulations and fluid damping which may become relevant at high frequencies. The uncoupled structural model may consider radiation damping either as a modal damping or as a viscoelastic bedding. Finally, structures which utilize acoustic radiation damping will be developed and investigated.