A gas turbine engine, comprising: an engine housing; a rotor assembly disposed within the engine housing; a rotor bearing supporting the rotor assembly within the engine housing; and an annular bearing support damper (60, 160) positioned between the rotor bearing and the engine housing, the annular bearing support damper (60, 160) comprising: an annular housing assembly (62, 168) fixedly coupled to the engine housing; a damping fluid annulus (94, 182) formed within the annular housing assembly (62, 168) and fillable with a damping fluid; a centering spring (64, 162) having a fixed end portion (68, 163) coupled to the engine housing and having a floating end portion (66, 164); and an array of circumferentially-spaced damper pistons (90, 172); characterized in that the array of circumferentially-spaced damper pistons (90, 172) comprises piston caps (102, 174) in fluid communication with the damping fluid annulus (94, 182); and the annular bearing support damper (60, 160) further comprises a plurality of bellows (104, 178) sealingly coupled between the piston caps (102, 174) and the annular housing assembly (62, 168) to prevent damping fluid leakage from the damping fluid annulus (94, 182), while permitting translational and lateral movement of the damper pistons (90, 172) relative to the annular housing assembly (62, 128) in conjunction with radial movement of the floating end portion (66, 164) of the centering spring (64, 162). an engine housing; a rotor assembly disposed within the engine housing; a rotor bearing supporting the rotor assembly within the engine housing; and an annular bearing support damper (60, 160) positioned between the rotor bearing and the engine housing, the annular bearing support damper (60, 160) comprising: an annular housing assembly (62, 168) fixedly coupled to the engine housing; a damping fluid annulus (94, 182) formed within the annular housing assembly (62, 168) and fillable with a damping fluid; a centering spring (64, 162) having a fixed end portion (68, 163) coupled to the engine housing and having a floating end portion (66, 164); and an array of circumferentially-spaced damper pistons (90, 172); an annular housing assembly (62, 168) fixedly coupled to the engine housing; a damping fluid annulus (94, 182) formed within the annular housing assembly (62, 168) and fillable with a damping fluid; a centering spring (64, 162) having a fixed end portion (68, 163) coupled to the engine housing and having a floating end portion (66, 164); and an array of circumferentially-spaced damper pistons (90, 172); characterized in that the array of circumferentially-spaced damper pistons (90, 172) comprises piston caps (102, 174) in fluid communication with the damping fluid annulus (94, 182); and the annular bearing support damper (60, 160) further comprises a plurality of bellows (104, 178) sealingly coupled between the piston caps (102, 174) and the annular housing assembly (62, 168) to prevent damping fluid leakage from the damping fluid annulus (94, 182), while permitting translational and lateral movement of the damper pistons (90, 172) relative to the annular housing assembly (62, 128) in conjunction with radial movement of the floating end portion (66, 164) of the centering spring (64, 162).