Wave Finite Element Formulation of the Acoustic Transmission Through Complex Infinite Plates
A finite element based derivation of the transmission loss (TL) of anisotropic layered infinite plates is presented in this paper. The wave finite element method (WFE) is used to represent the plate with a finite element model of a single unit cell. The incident acoustic field is a known plane wave, and the reflected and transmitted pressures are supposed to be plane waves with unknown amplitudes and phases. The periodicity conditions on the unit cell allow to find a simple matrix equation linking the amplitudes of the transmitted and reflected fields as a function of the incident one. This approach is validated for several cases against classical analytical models for thin plates and sandwich constructions, where the results agree perfectly for a reasonable mesh size. The method is then used to study the effect of stacking order in a laminated composite plate. The main interest of the method is the use of finite elements, which enables a relative easy modelling since most packages readily include different formulations, compared to analytical models, where different formulations have to be implemented for every kind of material.