Systems and methods for reducing noise in aircraft fuselages and other structures are described herein. A noise reduction system configured in accordance with one embodiment of the invention includes an auxetic core, a damping layer, and a constraining layer. In this embodiment, the auxetic core is supported by a structural member, and the damping layer is sandwiched between the auxetic core and the constraining layer. A method for manufacturing a structural assembly in accordance with another embodiment of the invention includes forming a stiffener by positioning a first ply of composite material against a first tool surface, positioning damping material against the first ply, and positioning a second ply of composite material against the damping material to sandwich the damping material between the first and second plies. The method can further include forming a skin by positioning a third ply of composite material against a second tool surface offset from the first tool surface, and attaching the stiffener to the skin by co-curing the first, second and third plies of composite material.