Frame structures can be coupled with external mechanical systems to improve their behavior under external loads. Some examples of such mechanical systems are oscillating masses working as tuned mass dampers, dynamic mass absorbers, elasto-plastic dampers. Among the other possibilities, a rocking rigid block can be used to improve the seismic behavior of a frame structure. In this paper a two degree of freedom model is considered representative of a general frame structure. It is coupled with a rocking rigid block through a viscoelastic device, which connects the lower part of the structure with the top of the rocking block. Another viscoelastic device connects the block to the ground. A Lagrangian approach is used to derive the nonlinear equations of motion that are then solved numerically. A simulation campaign is performed to analyze the seismic behavior of the coupled system by considering several registered earthquakes. In the analyses, the presence of the rocking rigid block is assumed to be beneficial for the system if the coupling of the frame structure with the rocking rigid block reduces the absolute displacements and/or the inter-story drifts. An extensive parametric analysis is performed varying the geometric characteristics of the block and the constitutive behavior of the visco-elastic devices. The results of such analyses are presented through behavior maps. For each of the parameters varied in the analyses, the corresponding value on the map provides the ratio between the displacements (or inter-story drifts) of the coupled system and of the frame not coupled with the rigid block. Such maps allow an immediate understanding of the effects of the block that has a beneficial effect when the ratio of the displacements is less than unity. Results reveal that in large ranges of the parameters’ values the rocking rigid block improves the seismic response of the frame structure.
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