The present invention relates to a bearing assembly (1) for a rotatable shaft (2). The bearing assembly comprises a bearing housing (10); a bearing (20) located within the bearing housing (10) and arranged in use to receive a rotatable shaft (2); and a damper (14) that couples the bearing (20) to the bearing housing (10) for damping vibrations of the rotatable shaft (2). The damper (14) comprises a shape memory alloy (40). This arrangement allows the bearing assembly to damp vibrations of the rotatable shaft.