Combining the 2.5D FE-BE method and the TMM method to study the vibro-acoustics of acoustically treated rib-stiffened panels

This paper is concerned with the prediction of the vibro-acoustic behavior of rib-stiffened panels treated with multiple layers of porous materials. The acoustically treated rib-stiffened panels are assumed to be uniform and infinitely long in one direction (the longitudinal direction) but the cross-section can have an arbitrary and often complicated shape. Although the two-and-half dimensional structural finite element method (2.5D FEM) and the two-and-half dimensional acoustic boundary element method (2.5D BEM) may be combined to perform the vibro-acoustic prediction, the presence of the multiple layers of acoustic treatment often makes the prediction too time-consuming. More efficient methods are required for such structures and the aim of this paper is to propose such a method. The rib-stiffened panel and the fluid domain containing the incident and reflected sound waves are modelled using 2.5D FEM-BEM while the acoustic treatment layer and the fluid domain containing the transmitted sound waves are dealt with, approximately, using the transfer matrix method (TMM). The coupling of TMM and 2.5D FEM-BEM is formulated in detail. Since the acoustically treated panel is assumed to be flat and baffled, the 2.5D BEM is based on the Rayleigh integral in the wavenumber domain. Meanwhile, the TMM is based on a two-dimensional Fourier transform which implies that the porous layers also extend to cover the baffle; the validity of this assumption is explored. The accuracy and efficiency of the method is compared with a full 2.5D FE-BE method for a homogeneous plate with attached layers of absorbent material. It is shown that the method proposed in this paper can reduce calculation time by about a factor of three compared with the full 2.5D FE-BE method. The proposed method is then applied to study the sound transmission loss (STL) of a typical rib-stiffened panel from a train carriage which is acoustically treated with different porous material layers, demonstrating that the design of the acoustic treatment can have a significant effect on the STL of the panel.