Solid panels with additional poro-elastic materials are widely used in engineering, mainly for sound insulation. In many cases, the panels are constructed in such a way that they can be idealised to be infinitely long and uniform in one direction, forming a so-called two-and-a-half dimensional (2.5D) structure. Although the 2.5D finite element and boundary element methods (FEM-BEM) are particularly suitable for predicting the vibro-acoustic behaviour of such structures, up to now the presence of poro-elastic media have not been adequately considered. In this paper a 2.5D FE-BE vibro-acoustic model is presented which accounts for solids, fluids and poro-elastic media. The poro-elastic media are modelled using the 2.5D FE approach based on the mixed displacement-pressure formulation of Biot's theory. The solids are also modelled using the 2.5D FE method but based on the linear theory of elasticity. The internal fluids are modelled using the 2.5D FE method as well. For a flat panel, the external fluid on both sides of the panel can be modelled using the 2.5D BE method based on the Rayleigh integral. The coupling between the various sub-models is derived in detail. The accuracy of the model is demonstrated by applying it to simple multi-layered structures for which solutions can be produced using other well-established methods. It is demonstrated that the elasticity of the solid frame of a porous medium has a great influence on the vibro-acoustics of a structure containing the porous material. The method is then applied to investigate the sound transmission loss (STL) of a typical railway vehicle floor structure. Results show that STL can be greatly improved by proper arrangement of porous material layers between the interior wooden floor and the outer extrusion; however, the load bearing supporting beams may significantly reduce the benefit of the porous material layers.

具有附加孔隙弹性材料的实心面板广泛用于工程中，主要用于隔音。在许多情况下，面板的构造应使其理想化，以使其在一个方向上无限长且均匀，从而形成所谓的二维半（2.5D）结构。尽管2.5D有限元和边界元方法（FEM-BEM）特别适合于预测此类结构的振动声行为，但到目前为止，尚未充分考虑孔隙弹性介质的存在。在本文中，提出了一个2.5D FE-BE振动声学模型，该模型考虑了固体，流体和孔隙弹性介质。基于Biot理论的混合位移-压力公式，使用2.5D FE方法对孔隙弹性介质进行建模。实体也使用2进行建模。5D FE方法，但基于线性弹性理论。内部流体也使用2.5D FE方法建模。对于平板，可以使用基于瑞利积分的2.5D BE方法对面板两侧的外部流体进行建模。详细推导了各个子模型之间的耦合。将模型应用于简单的多层结构即可证明模型的准确性，可以使用其他公认的方法为其生成解决方案。已经证明，多孔介质的实心框架的弹性对包含多孔材料的结构的振动声学有很大影响。然后将该方法应用于调查典型的铁路车辆地板结构的传声损耗（STL）。结果表明，通过在内部木地板和外部挤压物之间适当布置多孔材料层，可以极大地改善STL。但是，承重支撑梁可能会大大降低多孔材料层的优势。