A noise attenuation panel for a structure within a propulsion system includes a first plurality of unit cells; and a second plurality of unit cells, the second plurality of unit cells merged within the first plurality of unit cells, the first plurality of unit cells including a first periodic structure having a first unit cell, a second unit cell, a third unit cell and a fourth unit cell, each of the first unit cell, the second unit cell, the third unit cell and the fourth unit cell including a central body interconnected via a plurality of lateral tubes extending from the central body, the first periodic structure forming a first lateral layer of unit cells.