Combined Use of Rocking Walls and Inerters to Improve the Seismic Response of Frame Structures

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 both the frame and wall. This innovative mechanical assemblage is introduced by means of a reduced-order three-degrees of freedom model. The latter is constituted by a two-degree of freedom linear system, used as a model for a multistory frame structure, and a rigid block, which represents the rocking wall. The frame-wall connection is represented by an elastic link that spans the top of the block to the first story of the frame structure. Some inerters attached to both the frame and the block are considered to provide some apparent inertia forces. 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 coupled and uncoupled systems, thus providing a measure of the seismic enhancements that derive 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 coupling with block, thus enabling the use of smaller blocks. Finally, the proposed procedure, based on the spectrum-compatibility criterion, appears able to serve as a useful preliminary design tool for selecting the main characteristics of a system.