Abstract: Embodiments of a gas turbine engine are provided, as are embodiments of an annular bearing support damper and embodiments of a method for manufacturing an annular bearing support damper. In one embodiment, the gas turbine engine includes engine housing and a rotor assembly disposed within the engine housing. A rotor bearing supports the rotor assembly within the engine housing, and an annular bearing support damper is positioned between the rotor bearing and the engine housing. The support damper includes an annular housing assembly having a damping fluid annulus. An array of circumferentially-spaced damper pistons is movably coupled to the annular housing assembly and fluidly communicates with the damping fluid annulus. The damper pistons are fixedly coupled to the rotor bearing and moves in conjunction therewith to force the flow of damping fluid around the annulus during engine operation to reduce the transmissions of vibrations to the engine housing.