An example method for manufacturing a multicellular structure for acoustic damping is described that includes applying a porogen material to a solid support, inserting a multicellular frame into the solid support and through the porogen material so as to fill cells of the multicellular frame with the porogen material, fusing the porogen material, removing the multicellular frame from the solid support, and the multicellular frame contains a suspended fused porogen network attached to walls of the cells of the multicellular frame. The method also includes applying a solution to the suspended fused porogen network in the cells of the multicellular frame to percolate the suspended fused porogen network, curing the solution, and removing the suspended fused porogen network from the multicellular frame resulting in porous septum membranes of the cured solution in cells of the multicellular frame.