Vibration damping of large structures induced by attached small resonant structures

The paper presents a simple deterministic derivation of the vibration damping induced in a large main structure by a multitude of small substructures attached more-or-less compliantly to the main structure, each dissipating vibratory power at its frequencies of resonance. A simple expression is obtained for the damping induced in the large structure indicating that the damping depends primarily on the total effective mass of substructures resonating within a band centered at the frequency pf vibration, and is relatively independent of the damping factors of the individual substructures. The application of this simple expression for induced damping is illustrated by calculating the damping induced by substructures attached to an axially vibrating rod and to a flexurally vibrating beam. For the latter case, the calculated damping factors are compared with measured values.