Characterization of porous acoustic materials. State of the art

The theoretical model that is currently being used is based on the equations developed by M.A.Biot in 1956. The original Biot model was designed to sound propagation in water saturated porous rocks, but has later been adapted to include the physical effects that occur in sound absorbing materials. The model predicts two longitudinal waves and one shear wave. The phase velocities and amplitudes of these waves can be calculated as a function of the material parameters and the way the material is excited. In a crude approximation, one longitudinal wave will propagate in the frame of the material, its phase velocity being largely determined by the elastic coefficients of the frame and its apparent density. This wave is excited efficiently if the frame of the material is in direct contact with a vibrating plate for instance. The second longitudinal wave propagates mainly in the air in the pores. Its phase velocity depends on the compressibility of the air in the pores (which may differ from the adiabatic value due to thermal effects in the pores) and the apparent density of the air in the pores (which may differ from the density of free air due to viscous and inertial effects in the pores). This wave is generally excited efficiently by a sound wave impinging on the free surface of the material. At low frequencies, or for materials with a low permeability, it is not always possible to identify the two longitudinal waves as a ‘mechanical’ and an ‘air’ wave. The shear wave is mainly supported by the frame, the air in the pores having only a minor influence on its phase velocity [7].