A two-and-half dimensional finite element/boundary element model for predicting the vibro-acoustic behaviour of panels with poro-elastic media

Abstract 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.