A method facilitates assembling a flap system for a gas turbine engine exhaust nozzle including at least one backbone assembly. The method comprises providing a basesheet including a pair of circumferentially-spaced sides coupled together by an upstream side and a downstream side, forming at least one relief cut in the basesheet that extends at least partially across the basesheet from at least one of the circumferentially-spaced sides, and coupling the basesheet to the backbone assembly.