Analysis of wave propagation and absorption at oblique and normal incidence in poroelastic layers with active periodic inclusions

The work presents numerical studies of wave propagation under oblique and normal incidence in sound absorbing layers of poroelastic composites with active and passive inclusions embedded periodically along the composite layer surface. The purpose of active inclusions is to increase the spring-mass effect of the (passive) inclusions fixed to the elastic skeleton of the poroelastic matrix in order to increase the mechanisms of dissipation of acoustic waves penetrating such absorbing poroelastic composite layers. Finite element modelling is applied which involves the coupled models of Biot-Allard poroelasticity (for the poroelastic matrix), piezoelectricity and elasticity (for the active and passive inclusions), as well as the Helmholtz model for the adjacent layer of air. The Floquet?Bloch theorem is applied to allow for modelling of wave propagation at oblique incidence into the periodic composite layer. Moreover, since the actively exited piezoelectric inclusions become additional (though secondary) sources for wave propagation, the main acoustic waves that propagate into the poroelastic layer are modelled using incident background pressure fields in the air, which simulate plane waves propagating in the specified directions (oblique or normal to the poroelastic layer surface), and consequently, a perfectly matched layer is also attached to the air layer to simulate an open boundary condition on that side of the air layer. Some results of such complex numerical models are confronted with the corresponding results found with more classical approaches, i.e., without Floquet-Bloch periodicity for the case of normal incidence, and with a pressure boundary condition instead of the background field and perfectly matched layer.