The coupling of structures with tuned mass dampers, dynamic mass absorbers, elastoplastic dampers, and rigid walls is effective in reducing displacements and drifts of frame structures under external loads. This paper analyses the effectiveness of connecting the first storey of a frame structure to an external structure shorter than the frame structure by a visco-elastic device. Two alternative visco-elastic devices are considered for the coupling, they are modelled with the Kelvin–Voigt and Maxwell constitutive laws, respectively. Additionally, an inerter device is applied to the external structure to modify its inertial force and increase the effectiveness of the coupling. The coupled structure is modelled as a three-degree-of-freedom mechanical system, and its equations of motion are obtained by a direct approach. The coupling with the external structure is considered beneficial for the frame structure if the absolute displacements of the coupling level or the inter-storey drifts reduce compared to those of the stand-alone frame structure. A preliminary modal analysis shows that the coupling with the external structure equipped with the inerter device improves the dynamic and seismic performances of the system. A further analysis is performed by considering four ground motion records. The results, organized in maps, confirm that the coupling with the external structure reduces the displacements and drifts of the frame structure in large ranges of values of the parameters that characterize the external structure and connection device.
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