A 3-D finite element model for sound transmission through a double-plate system with isotropic elastic porous materials

Abstract

The prediction of sound transmission through multilayer structures is of utmost importance in aircrafts, buildings, and other engineering applications. In view of optimizing the transmission loss, the finite element method is an interesting mean to model such structures since it permits one to account for complex structure geometries and to model accurately the boundary conditions. In this paper, a 3-D-finite element model is developed to evaluate the normal incidence transmission loss through a double-plate system with cavity absorption. The cavity is filled with an air-saturated isotropic elastic porous materials. The model uses a two-field finite element procedure for the porous medium based on the Biot theory. Since the Biot theory considers only the energy dissipation due to the viscous effects, the frequency-dependent bulk modulus of the air, worked out by Champoux and Allard [J. Appl. Phys. 70, 2182–2191 (1991)], is adopted to account for the energy dissipation due to thermal exchanges. Also, two sets of field variables are considered: the u-U and the u-P sets, where u and U are the solid and fluid displacements and P is the pore-fluid pressure. Both approaches are developed and compared through numerical simulations. [Work supported by Bombardier, Inc., Canadair, and N.S.E.R.C.]