Multi-scale computation of sound absorbing materials

The multi-scale computation method has been treated for acoustical purposes, for controlling the chain of parameters including the relations between the microscopic, macroscopic and acoustic parameters of sound absorbing materials. Possible anisotropic behaviour of materials has been taken into account. The macro-scale parameters complex density and complex compressibility are produced by the multi-scale computation. Their imaginary parts are due to the viscous and thermal losses of the fluid in porous materials. The deviations of their real parts from their physical values take into account some other things affecting the sound propagation in porous materials. The macro-scale complex parameters can be defined using two alternative ways: the direct numerical approach and the hybrid numerical approach. In the former, the complex density and compressibility are directly formed from the calculated dynamic viscous and thermal permeabil-ity functions. In the latter, static viscous and thermal permeability functions, three tortuosity functions (the strict amount depending on the selection from three possible models), and the viscous and thermal characteristic lengths, are computed, from which the complex density and compressibility are finally calculated. From the complex density and compressibility, the imped-ance and the complex wave number for rigid frame models are computed similarly in both of the methods. In the Biot model, the viscous and thermal effects are coupled, so the logic pre-sented for the rigid frame models cannot be directly. However, the effective compressibility and the dynamic viscous tortuosity, based on either of the approaches, can directly be included in the parameters of the Biot model, to take into account the viscous and thermal properties of the fluid phase.