Damped highly stressed engineering components are disclosed. The disclosed inventive concept provides a method and system for increasing the damping capacity of an engineering system by adding a non-flat solid, highly damped insert to a system component that contributes most to the system's dynamic response. A friction damped insert can either be embedded into the damped components during casting or fastened to the outer surface of the damped component. The insert is made of the single layer of flexible material by forming it into a rigid elongated body. The layer of material can be turned over on itself without folding to create a cylinder or can be folded over a number of times to create a prismatic bar. The layer of material may be shaped into a corrugated panel. The layer of flexible material may have a number of relatively small openings or perforations with a uniform spatial distribution.