Optimum response control of multi-degree-of-freedom seismic control system incorporated with concentratedly arrenged tuned viscous mass dampers

A tuned mass damper-like system can be constructed by arranging a two-node mechanical mass device, referred to as an inerter or a dynamic mass, that generates inertial resistance forces proportional to the relative accelerations between its two nodes with a viscous element in parallel and spring element in series arrangement. The present system is referred to as the tuned viscous mass damper (TVMD) seismic control system When TVMDs are incorporated into a building structure subjected to strong ground motions, components of the inter-story motions resonant to the additional system result in amplified motions and substantial energy dissipation in the viscous element. For a multi-degree-of-freedom (MDOF) system a closed form optimum design is obtained from equivalent single-degree-of-freedom reduction using the fundamental mode of an uncontrolled system if the apparent mass distribution of the dampers is proportional to that of the primary stiffnesses. The optimum design, however, does not apply to a system in which the distribution of the supplemental masses is non-proportional to that of the primary stillnesses. Thus, the main objective of this paper is to discuss the optimum control method and characteristics of an MDOF seismic control system having non-proportionally distributed TVMDs.