Designing phononic crystals to improve viscous absorption at low frequencies

This work reviews configurations of phononic crystals specially designed to enhance viscous absorption at low frequencies. The phononic crystals are made of two-dimensional distributions of cylindrical rods with circular sections embedded in air. A homogenization theory has been developed to easily study the case of finite structures of large dimensions. The theory provides analytical expressions for the effective size of the structure, effective mass density, effective sound speed, and effective viscosity. Results are reported for semi-infinite slabs, finite clusters, and superstructures denominated as super-crystals consisting of phononic crystals with two different lattice periods. It is shown that the filling fraction is a key factor in determining the maximum absorption of crystals made with cylinders having the same diameter. For super-crystals, the combination of two lattice periods produces a decay coefficient faster than that of the crystal made with smaller cylinders. Experimental data support the results predicted by the theory.