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Dispersion diagrams I − free/free assumption. (A) Schematic representation of the FE models for the ordinary and (B) hierarchical large-scale metamaterial (the inset provides an enlargement of the region where the second hierarchical level is introduced) under the assumption of free-free boundary conditions (BCs) applied to the top and bottom surfaces of the unit cell and periodic boundary conditions (PBCs) at lateral surfaces. Dispersion curves of the (C) ordinary and (D) hierarchical large-scale elastic metamaterial, showing a remarkable enhancement of the width of the BGs (orange rectangles) and their shift towards lower frequencies. Geometrical parameters of the unit cells for both ordinary and hierarchical structure are provided in the text.
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