An apparatus comprising: a static engine structure ; at least one shaft (40; 50; 106) that rotates relative to the static engine structure ; and a bearing assembly that supports the shaft (40; 50; 106), wherein the bearing assembly includes at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure , at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one second bearing includes a damper , and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper , wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure , and wherein the at least one second bearing is downstream of the at least one first bearing , the at least one third bearing is downstream of the at least one second bearing , and the at least one fourth bearing is downstream of the at least one third bearing ; and characterised by the at least one fourth bearing including an inner race that has a first centerline (C1) and an eccentric outer race that has a second centerline (C2) that is radially offset from the first centerline (C1). a static engine structure ; at least one shaft (40; 50; 106) that rotates relative to the static engine structure ; and a bearing assembly that supports the shaft (40; 50; 106), wherein the bearing assembly includes at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure , at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one second bearing includes a damper , and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper , wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure , and wherein the at least one second bearing is downstream of the at least one first bearing , the at least one third bearing is downstream of the at least one second bearing , and the at least one fourth bearing is downstream of the at least one third bearing ; and characterised by the at least one fourth bearing including an inner race that has a first centerline (C1) and an eccentric outer race that has a second centerline (C2) that is radially offset from the first centerline (C1). at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure , at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one second bearing includes a damper , and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure , wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper , wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure , and wherein the at least one second bearing is downstream of the at least one first bearing , the at least one third bearing is downstream of the at least one second bearing , and the at least one fourth bearing is downstream of the at least one third bearing ; and characterised by the at least one fourth bearing including an inner race that has a first centerline (C1) and an eccentric outer race that has a second centerline (C2) that is radially offset from the first centerline (C1). <EOS>