Wave and finite element method for predicting sound transmission through finite multi-layered structures with fluid layers

In this paper, a modelling strategy is proposed to predict sound transmission loss (STL) of multi-layered panels with fluid layers based on a wave and finite element method. This method starts with meshing a small segment of each solid layer through the thickness to find the mass and stiffness matrices using a conventional finite element method. The acoustic pressures applied on the structure by the fluids surrounding and inside the structure are discretized into external nodal forces. By post-processing the matrices using equilibrium conditions and periodic structure theory, the spectral dynamic stiffness matrices (DSM) of solid layers are derived in the wavenumber domain. By assembling these matrices with those of fluid layers, which are derived analytically, a total spectral DSM is found and used to calculate the response to incident acoustic waves. To take account of the effect of the finite size of a structure, a spatial windowing technique is applied. Various numerical examples are presented to validate this method. For simple structures, analytical methods are available for comparison. For complicated structures, using analytical methods is difficult and the proposed method becomes valuable. Results are compared with measurements. The method is seen to give accurate predictions at little computational cost.