Structblock

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 non-linear 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

This paper investigates the possibility to enhance the seismic response of a frame structure by the combined use of an external rocking wall and some inerters attached to the frame and to the wall as well. This innovative mechanical assemblage is here introduced by means of a reduced order 3-\textit{DOF} model. This latter is constituted by a two-degree of freedom linear system, used as a model for a multi-story frame structure, and by a rigid block, which represents the rocking wall. The frame-wall connection is represented by an elastic link spanning from the top of the block to the first story of the frame structure. Such a mechanical system, already studied by the Authors in other papers, is here enriched by the introduction of some inerters attached to both the frame and the block, in order to have some apparent inertia forces. For this model, the nonlinear equations of motion are obtained and successively numerically integrated, considering seismic base motions. An extensive parametric analysis is performed and the results are summarized in gain maps that show the ratio of the maximum displacements or drifts of the coupled and uncoupled systems, thus providing a measure of the seismic enhancements deriving from the coupling. It is found that there are wide regions of the adopted base parameters where coupling is effective. Results also show that the use of inerters increases the effectiveness of the coupling with the block, thus allowing to use of smaller blocks. Finally, the proposed procedure based on spectrum compatibility criterion appears able to provide a useful preliminary design tool to choose the main characteristics of the system.

In this paper the linear elastic coupling between a 2 degree of freedom shear-type frame system and a rigid block is analytically and experimentally investigated. As demonstrated by some of the authors in previous papers, it is possible to choose a coupling system able to guarantee advantages, whatever the mechanical characteristics of the frame. The main purpose of the investigation is to validate the analytical model. The nonlinear equations of motion of the coupled system are obtained by a Lagrangian approach and successively numerically integrated under harmonic and seismic excitation. The results, in terms of gain graphs, maps and spectra, represent the ratio between the maximum displacements or drifts of the coupled and uncoupled systems as a function of the system's parameters. Numerical investigations show the effectiveness of the nonlinear coupling for a large set of parameters. Thus experimental tests are carried out to verify the analytical results. An electro-dynamic long-stroke shaker sinusoidally and seismically forces a shear-type 2 d.o.f frame coupled with a rigid aluminium block. The experimental investigations confirm the effectiveness of the coupling as predicted by the analytical model.