A structural damping assembly includes a bonding plate, a stiffener layer, an elastomeric layer, and a constraining layer. The elastomeric layer is boned between the stiffener layer and the constraining layer. The bonding plate and the stiffener layer extend between, and are preferably in contact with, webs which form a pocket on a substrate such as a transmission support beam. The structural damping assembly uses the energy dissipating properties of the elastomeric layer that is sandwiched between the vibrating stiffener layer and the constraining layer to combat noise due to resonant response while operating as a stiffener that increases the frequency of resonance to a range where coincidental placement with an excitation frequency is reduced.