We consider acoustic wave propagation through a periodic array of the inclusions arbitrary shape. The inclusion size is much smaller than period while wavelength fixed. derive and rigorously justify dispersion relation for general frequencies show that there are exceptional which solution cluster waves propagating in different directions with so cannot be defined uniquely. Examples provided sph...

We address the homogenisation of a linear viscoelastic and hierarchical composite material in one-dimensional (1D) framework via three-scale asymptotic method. consider family heterogeneous problems with periodic, rapidly-oscillating piece-wise coefficients that model structure two levels organisation. Here, we assume continuity contact conditions at interfaces among constituents set straightfo...