A tuning criterion for the inertial tuned damper. Design using phasors in the Argand-Gauss plane

A new approach to the design of a dynamic damper for a monomass oscillator is presented; the design procedure is then applied to control a multimodal oscillator. This new dynamics emerged from an analysis by means of phasors (rotating vectors in the Argand-Gauss plane) which revealed the phase relat ions between the damper and main oscillator. In particular this work introd uces a geometric formalism, based on the use of phasors in the complex plan e, for the sizing of inertial dampers applied to multimodal structural osci llators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass b y 90 degrees, 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 serves to limit the displacement of main oscillator. Our geom etrical approach provides a method whose language is close to that of struc tural mechanics, thus paving the way to the professionals for: (i) sizing t he damper parameters and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is that of explorin g the use of dampers to control the response of buildings under horizontal seismic and aerodynamic loads. (C) 1999 Elsevier Science Inc. All rights re served.