A Scalable Framework for Simultaneously Optimizing Damper Positions and Viscosities

We consider damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine the damping positions and viscosity values of the dampers in the system so that they produce the lowest average total energy. We propose a new framework for determining the number and positions of the dampers, using re-weighted $l_1$ minimization and pruning techniques. The efficiency and performance of our new approach are verified and illustrated in several numerical examples.