Optimum distribution of additive damping for vibrating beams

Cost and weight effectiveness of concentrated and distributed additive damping is studied for linear systems (discrete and continuous) under prescribed harmonic loads and/or displacements. Stiffness and mass changes due to additive damping are included. From a numerical example studied it can be concluded that optimal damping distributions can reduce resonant responses by about 40% as compared to uniformly distributed damping of the same cost or weight. The optimization technique as well as an exact displacement method for analysis of harmonically vibrating beams and frames are presented.