Seismic design of passive tuned mass damper parameters using active control algorithm

Tuned mass dampers are a widely-accepted control method to effectively reduce the vibrations of tall buildings. A tuned mass damper employs a damped harmonic oscillator with specific dynamic characteristics, thus the response of structures can be regulated by the additive dynamics. The additive dynamics are, however, similar to the feedback control system in active control. Therefore, the objective of this study is to develop a new tuned mass damper design procedure based on the active control algorithm, i.e., the H2/LQG control. This design facilitates the similarity of feedback control in the active control algorithm to determine the spring and damper in a tuned mass damper. Given a mass ratio between the damper and structure, the stiffness and damping coefficient of the tuned mass damper are derived by minimizing the response objective function of the primary structure, where the structural properties are known. Varying a single weighting in this objective function yields the optimal TMD design when the minimum peak in the displacement transfer function of the structure with the TMD is met. This study examines various objective functions as well as derives the associated equations to compute the stiffness and damping coefficient. The relationship between the primary structure and optimal tuned mass damper is parametrically studied. Performance is evaluated by exploring the h2-and h∞-norms of displacements and accelerations of the primary structure. In time-domain analysis, the damping effectiveness of the tune mass damper controlled structures is investigated under impulse excitation. Structures with the optimal tuned mass dampers are also assessed under seismic excitation. As a result, the proposed design procedure produces an effective tuned mass damper to be employed in a structure against earthquakes.