Numerical Models for the Scattering Properties of Multilayered Structures With Periodic Cells

ABSTRACT The objective of this work is to model the acoustic response of multilayered structures composed of both homogeneous layers and periodic cells so as to obtain their scattering properties (i.e., reflection and transmission coefficients). The host material of each layer is either elastic, fluid, or poroelastic. The homogeneous layers are modelled with waves, while the periodic layers are modelled with higher‐order FEM. Two modelling methods from the literature, the Global Method and the Transfer Matrix Method, initially dedicated to the modelling of stacks of homogeneous layers, are extended. They are then tested on examples from the literature or adaptations thereof, to cover a complete panel of test configurations. Additionally, a comparison of results obtained via a commercial finite element software is proposed. Results confirm that the methods are well suited to higher‐order finite elements and also show that, while the method derived from the Transfer Matrix Method suffers from stability issues, those derived from the Global Method remain stable for all studied configurations.