Mitigation of three-dimensional vibrations of a frame structure using magneto-rheological dampers

An analytical discrete model is formulated to study the three-dimensional dynamical response of a prototype beam frame, reproducing the structural behaviour of a two-storey building. Once proper geometric constraints are introduced, and the rotations of the beam-column nodes are condensed through a Guyan reduction, the model possesses six degrees of freedom, corresponding to the barycentric planar displacements of each storey. The model also allows the description of eccentric masses which break the structural symmetry. The passive controlling action of two magnetorheological dampers is considered. Their hysteretic behavior is described by a modified Bouc-Wen rheological model. The dampers apply two eccentric and independent forces, acting on the first-storey displacements. The chosen set-up allows the mitigation of both the lateral and torsional motion when monodirectional ground motion is imposed on the non-symmetric structure. Numerical investigations on the seismic response to natural accelerograms are presented. The effectiveness of the passive control strategy is discussed through synthetic performance indexes, for both the symmetric and the non-symmetric structure