A process for manufacturing a composite structure includes: providing first mandrels, each first mandrel including a base and a plurality of projections arranged longitudinally along and projecting vertically out from the base; providing second mandrels; providing first ribbon plies, each first ribbon ply including a sheet of fibrous material; arranging each first ribbon ply with a respective first mandrel, the arranging of each first ribbon ply including substantially covering each surface of each of the projections of one of the first mandrels with a respective first ribbon ply; mating each second mandrel with a respective first mandrel such that each first ribbon ply is sandwiched between a respective first mandrel and a respective second mandrel; and curing resin disposed with the first ribbon plies to consolidate the first ribbon plies together and form a fiber-reinforced composite core structure of an acoustic panel.