A gas turbine engine rotor tip clearance and shaft dynamics system, comprising: a gas turbine engine including: an engine case; a rotor (134, 136) disposed within the engine case; a rotor bearing assembly disposed within the engine case and rotationally mounting the rotor (134, 136) therein; a plurality of vibration isolators mounted on, and external to, the engine case and coupled to the rotor bearing assembly, each vibration isolator configured to provide linear and independently tunable stiffness and damping; a plurality of actuators; an actuator control; and a support structure coupled to, and extending between, each vibration isolator and the rotor bearing assembly, the gas turbine engine includes a turbine section including a high pressure turbine and a low pressure turbine and having a gas flow path, and the support structure includes a strut that traverses the gas flow path between the high pressure turbine and the low pressure turbine; wherein: each vibration isolator comprises a plurality of adjustment devices (410-1, 410-2) adjustably coupling the vibration isolator to the rotor bearing assembly; each vibration isolator comprises: a first flexural member; a second flexural member; an orifice; and a housing assembly; the first and second flexural members are coupled via the adjustment devices and connection hardware to the strut and thus to the rotor bearing assembly; the second flexural member and the housing assembly are spaced apart from each other to define a fluid cavity that is in fluid communication with the orifice which extends through the housing assembly and is in fluid communication with a fluid reservoir within which is disposed an incompressible hydraulic fluid filling the orifice and the fluid cavity; and each actuator is coupled to one of the vibration isolators and is responsive to actuation control signals to actively control rotor position and rotor dynamics, the actuator control being operable to selectively supply the actuation control signals to each actuator. an engine case; a rotor (134, 136) disposed within the engine case; a rotor bearing assembly disposed within the engine case and rotationally mounting the rotor (134, 136) therein; a plurality of vibration isolators mounted on, and external to, the engine case and coupled to the rotor bearing assembly, each vibration isolator configured to provide linear and independently tunable stiffness and damping; a plurality of actuators; an actuator control; and a support structure coupled to, and extending between, each vibration isolator and the rotor bearing assembly, the gas turbine engine includes a turbine section including a high pressure turbine and a low pressure turbine and having a gas flow path, and the support structure includes a strut that traverses the gas flow path between the high pressure turbine and the low pressure turbine; wherein: each vibration isolator comprises a plurality of adjustment devices (410-1, 410-2) adjustably coupling the vibration isolator to the rotor bearing assembly; each vibration isolator comprises: a first flexural member; a second flexural member; an orifice; and a housing assembly; the first and second flexural members are coupled via the adjustment devices and connection hardware to the strut and thus to the rotor bearing assembly; the second flexural member and the housing assembly are spaced apart from each other to define a fluid cavity that is in fluid communication with the orifice which extends through the housing assembly and is in fluid communication with a fluid reservoir within which is disposed an incompressible hydraulic fluid filling the orifice and the fluid cavity; and each actuator is coupled to one of the vibration isolators and is responsive to actuation control signals to actively control rotor position and rotor dynamics, the actuator control being operable to selectively supply the actuation control signals to each actuator. each vibration isolator comprises a plurality of adjustment devices (410-1, 410-2) adjustably coupling the vibration isolator to the rotor bearing assembly; each vibration isolator comprises: a first flexural member; a second flexural member; an orifice; and a housing assembly; a first flexural member; a second flexural member; an orifice; and a housing assembly; the first and second flexural members are coupled via the adjustment devices and connection hardware to the strut and thus to the rotor bearing assembly; the second flexural member and the housing assembly are spaced apart from each other to define a fluid cavity that is in fluid communication with the orifice which extends through the housing assembly and is in fluid communication with a fluid reservoir within which is disposed an incompressible hydraulic fluid filling the orifice and the fluid cavity; and each actuator is coupled to one of the vibration isolators and is responsive to actuation control signals to actively control rotor position and rotor dynamics, the actuator control being operable to selectively supply the actuation control signals to each actuator.