Deliberate introduction of acoustic radiation damping using locally resonant materials

许多轻质结构都是刚性且阻尼弱的。这一观察结果也适用于许多乐器和一些水下结构。这些结构的共同之处在于，声辐射阻尼可以具有与其他阻尼机构类似的甚至更高的量级。该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，尽管实际物理学需要耦合结构声学模型。然而，从数学上讲，结构声学模型可以简化为结构模型，其中 Schur 补集代表整个流体行为。该项目定量研究声辐射阻尼，旨在开发一种数学模型来考虑声辐射阻尼，而不解决声辐射问题。除了实际的辐射阻尼之外，定量估计还包括对声学 BEM 公式中出现的数值阻尼和流体阻尼的研究，这些阻尼可能在高频下变得相关。非耦合结构模型可以将辐射阻尼视为模态阻尼或粘弹性垫层。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.