Disclosed are a system for damping vibrations of a gas turbine exhaust and a method to damp vibrations of a gas turbine exhaust. The system includes a turbine exhaust cylinder connected to a turbine exhaust manifold establishing a fluid flow path, the fluid flow path including an inner and an outer flow path. A damping blanket damps the vibrations and is coupled to a surface of the inner flow path via a constraining layer clamped by a plurality of studs.