Continuous degree of freedom acoustic cores

A turbofan engine comprising:

• a fan rotor having a plurality of fan blades;
• a nacelle surrounding the fan rotor;
• a fan duct defined by the nacelle, the fan duct having a duct inner wall;
• and
• an acoustic liner positioned along the duct inner wall of the fan duct, the acoustic liner, comprising:
• a face sheet;
• a back sheet spaced from the face sheet;
• and
• a core layer defining a cellular structure disposed between the face sheet and the back sheet, the core layer comprising:
• a plurality of first resonant cells coupled to the back sheet, each of the first resonant cells comprising:
• a first cell wall coupled to the back sheet along a first cell wall base edge, the first cell wall extending from the back sheet toward the face sheet, the first cell wall further coupled to the face sheet along a first cell wall top edge,
• wherein the first cell wall of each of the first resonant cells comprises a surface extension that extends from a surface of the first cell wall.