Dynamic response of a linear two d.o. f system visco-elastically coupled with a rigid block

The present work investigates the use of a rigid rocking block as a tool to reduce vibrations in a frame structure. The study is based on a simplified model composed by a 2-DOF linear system, meant to represent a general M-DOF frame structure, coupled with a rocking rigid block through a linear visco-elastic device, which connects only the lower part of the 2-DOF system. The possibility to restrain the block directly to the ground, by means of a second visco-elastic device, is investigated as well. The dynamic response of the model under an harmonic base excitation is then analysed in order to evaluate the effectiveness of the coupling in reducing the displacements and the drift of the 2-DOF system. The nonlinear equations of motion of the coupled assemblage 2-DOF-block are obtained by a Lagrangian approach and then numerically integrated considering some reference mechanical and geometrical quantities as variable parameters. It follows an extensive parametric analysis, whose results are summarized through behaviour maps, which portray the ratio between the maximum displacements and drifts of the system, with and without the coupling with the rigid block, for several combinations of system's parameters. When the ratio of the displacements is less than unity, the coupling is considered effective. Results show that the presence of the rocking rigid block improves the dynamics of the system in large ranges of the characterizing parameters.