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In recent work, it has been shown that conventional sound absorbing materials (e.g., lightweight fibrous media) can provide structural damping when placed adjacent to vibrating structures, including infinite panels, partially-constrained panels and periodically-supported panels typical of aircraft structures. Thus, a fibrous layer may serve two functions at once: absorption of airborne sound and the reduction of structure-borne vibration. It has also been found that the damping is primarily effective below the critical frequency of the structure, and that the damping results from viscous interaction between the fibrous layer and the evanescent near-field of the panel, in the region where incompressible flow caused by the panel vibration oscillates primarily parallel with the panel surface.