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Numerical models. (A) Schematic representation of the FE models used for the calculation of the dispersion curves localized at the surface. Free boundary conditions are applied to the top surface of the unit cell and a semi-infinite half-space is modeled through 8λ-long soil-like domain + a 2λ-long PML region. For the sake of synthesis, only the hierarchical unit cell is reported. (B) Schematic representation of the FE models used for the transient calculations. In this case, only the non hierarchical model is reported. (C) Time evolution and frequency content of the input signals used in simulations: (left panel) a triangular-like excitation and 21-cycle Hanning window modulated sinusoidal tone bursts centered at (central panel) 3.8 Hz and (right panel) 2.4 Hz, respectively. The frequency spectrum clearly shows a rather broad-band and narrow-band frequency content, respectively. Displacement units are in decimeters [dm].
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