A tunable, mechanical and acoustical damping system is integrated into a lightweight composite aerospace vehicle structure. In one embodiment, the damping system (22) is incorporated into the wall of a spacecraft payload fairing (12) and includes an outer skin (24), a grid structure (26), an inner skin (28) and a tuning conduit (30). The grid structure (26) forms a number of cells (36) some of which may be interconnected. The cell volumes and the tuning conduit (30) are effective as a Helmholz resonator to reduce potentially damaging noise in the payload compartment (20) of the fairing (12). By appropriate selection of the conduit's dimensions in conjunction with the cell dimensions, the resulting resonator can be tuned to damp a selected frequency or frequencies. For example, a resonant frequency of the fairing (12) with its payload (18). A viscoelastic material (34) is provided between the grid structure (26) and inner skin (28) for mechanical damping. The system (22) can be implemented in lightweight composite materials and allows for SNAPSAT construction.