论文标题
定期穿孔的弹性板与流动相互作用的振动声传播的均质化
Homogenization of the vibro-acoustic transmission on periodically perforated elastic plates interacting with flow
论文作者
论文摘要
我们认为在存在永久性流的情况下，与刚性式穿孔板相互作用的无粘性流体中传播的声波。本文提出了一种通过嵌入板的薄透射层的渐近均匀化获得的声学界面的模型。为了解决流量，采用了稳定和波动部分中流体压力和速度的分解。这可以实现线性化和有效使用均质化方法，从而导致模型阶降低效应。扩展的Helmholtz方程对永久流的依赖性在穿孔板附近引入了局部周期性速度场，因此同质化界面的系数取决于流动。自然耦合条件扩展的派生模型提供了一个隐含的Dirichlet到Neumann操作员。波导中波传播的数值模拟说明了流速对声学传输的影响。还探索了一些几何方面。
We consider acoustic waves propagating in an inviscid fluid interacting with a rigid periodically perforated plate in the presence of permanent flows. The paper presents a model of an acoustic interface obtained by the asymptotic homogenization of a thin transmission layer in which the plate is embedded. To account for the flow, a decomposition of the fluid pressure and velocity in the steady and fluctuating parts is employed. This enables for a linearization and an efficient use of the homogenization method which leads to a model order reduction effect. The dependence of an extended Helmholtz equation on the permanent flow introduces a locally periodic velocity field in the perforated plate vicinity, so that the coefficients of the homogenized interface depend on the flow. The derived model extended by natural coupling conditions provides an implicit Dirichlet-to-Neumann operator. Numerical simulations of wave propagation in a waveguide illustrate the flow speed influence on the acoustic transmission. Also some geometrical aspects are explored.
