FEA for damping of structures having elastic bodies, viscoelastic bodies, porous media and gas

A numerical method is proposed to calculate damping properties for soundproof structures involving solid bodies, porous media and air in two-dimensional regions. Both effective density and bulk modulus have complex quantity to represent damped sound fields in the porous media. Particle displacements in the media are discretized using finite element method. For damped solid bodies, displacements are formulated using conventional finite elements including complex modulus of elasticity. Displacement vectors as common unknown variables are solved under coupled condition between solid bodies, porous media and gas. Further, by applying asymptotic method to complex eigenvalue problem, explicit expressions of modal loss factor for the mixed structures are derived. The proposed methods yield appropriate results for some typical problems and this method diminish computational time for large-scaled finite element models concerning the mixed structure. Moreover, it is found that damping can be coupled in the mixed structures between solid bodies, porous media and air.