modeling wave dispersion and band gaps in heterogeneous elastic media

In this paper we report recent developments and results concerning validation of the homogenization approach applied in modeling waves in strongly heterogeneous elastic media. The homogenization limit model is obtained for stationary waves, but can also be used to estimate dispersion properties for long guided waves propagation. Band gaps distribution depends on the material contrast and on the geometrical arrangements in the microstructure. Similarity between discrete structures and heterogeneous continua is used to demonstrate the dispersion phenomena. The modeling approach has been extended to the piezo-phononic materials, which may be useful in designing smart materials. Also problems of optimal shape design at the microscopic level were pursued.