Based on our previous work, we propose a homogenized model of acoustic waves propagating through periodically perforated elastic plates with metamaterial properties due to embedded arrays of soft elastic inclusions serving for resonators. Such structures enable to suppress the acoustic transmission for selected frequency bands. Homogenization of the vibro-acoustic fluid-structure interaction problem in a 3D complex geometry of the transmission layer leads to effective transmission conditions prescribed on the acoustic meta-surface associated with the mid-plane of the Reissner-Mindlin plate. Asymptotic analysis with respect to the layer thickness, proportional to the plate thickness and to the perforation period, yields an implicit Dirichlet-to-Neumann operator defined on the homogenized metasurface. An efficient method is proposed for computing frequency-dependent effective parameters involved in the homogenized model of the layer. These can change their signs, thus modifying the acoustic impedance and the effective mass of the metasurface. The global problem of the acoustic wave propagation in a waveguide fitted with the plate is solved using the finite element method. The homogenized interface allows for a significant reduction of the computational model. Numerical illustrations are presented.
翻译:根据我们先前的工作,我们提议了一个通过定期穿孔弹性板的声波传播的同质模型,由于软弹性内嵌阵列的软弹性内嵌阵列,这些结构能够抑制某些频率波段的声传。在3D复杂的传输层几何中,对振动-声波流结构互动问题进行同质处理,从而导致与Reisner-Mindlin板块的中间平面相联的声动元表上规定有效传输条件。关于层厚度、与板厚成比例和与穿孔期成比例的感应分析,产生一个在同质化元表层上定义的隐含的dirichlet-Neumann操作器。提出了一种高效的方法,用于计算同质模型所涉的频率独立有效参数。这些方法可以改变其信号,从而改变声阻力和元表的有效质量。在与板搭配的波导体中,全球声波波传播问题通过有限的模型方法得到解决。