Phasors-techniques design of inertial passive dampers for tower buildings. Stability and performance evaluations

This work introduces a geometric formalism, based on the use of phasors in the Argand-Gauss plane for the design and sizing of inertial dampers to be applied to multimodal structural oscillators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass to be controlled by 90°, so that the elastic force transmitted by the damper becomes a viscous force on the controlled oscillator. When such condition occurs we say that the damper is ‘tuned’ to the main oscillator; the damping induced by the damper is modest and serves only to limit the displacement of main oscillator.Our geometrical approach provides a method whose language is close to that of structural mechanics, thus paving the way to the professional for: (i) sizing the damper parameters; and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is explore the use of dampers to control the initial response modes of buildings under horizontal seismic and aerodynamic loads. Having introduced the concept of a monomass oscillator equivalent to a given mode of vibration, we develop a multimodal multidamper model which we then use to perform numerical evaluations. Several control strategies (involving changes in number and position of the dampers) are considered in relation to variation in bandwidth and intensity of the external forcing action. We discuss the advantages and limitations of this passive approach to structural control.