Étude vibroacoustique des matériaux poreux par éléments finis

Abstract

Poroelastic finite elements based on Biot displacement theory are examined in the context of vibroacoustic applications. First, convergence of linear finie elements is investigated. It is shown that mesh criteria usually used for monophasic elements can be applied considering Biot wavelengths, but are insufficient for 3-D applications. Next, experimental validations are then performed with a particular emphasis on the determination of the characteristics of the porous material (polymer foams) as input parameters for simulations. The first experiment concerns the impedance measurement of a vibrating porous sample in a duct. Various boundary conditions are carried out to test the validity of isotropic and transverse isotropic elasticity laws for the skeleton. The second experiment concerns the vibration of a simply supported plate damped by a porous layer. Although good tendencies are found, results emphasize the difficulty to determine accurately the viscoelastic tensor of the skeleton. The last part deals with the analysis of the behavior of poroelastic materials. A partition of reactive and dissipative powers is derived from the finite element formulation. Applied to the case of a porous layer bonded onto a plate, it shows the importance of viscoelastic dissipation in the skeleton. An equivalent plate model is then derived considering the porous layer as a viscoelastic layer subject to shear. Good results demonstrate the possibility to simplify the calculations concerning the vibration behavior of such structures.