Many researchers used low-dimensional mechanical models (also called archetype models) to capture the main dynamic and seismic aspects of real structures. For instance, two-Degree-Of-Freedom (2-DOF) models were used to study the conceptual aspects of the base isolation technique in [1] or of Tuned Mass Damper (TMD) system in [2]. Low-dimensional models were also used to investigate other structural schemes. Paper [3] investigated the dynamic behavior of a frame structure placed on a rocking podium with a low-dimensional model. Instead, an archetype model was used in [4] where the improvement of the dynamic and seismic performances of frame structures was obtained by connecting an external rocking wall to the first storey of the frame structures through a visco-elastic device. Finally, paper [5] used an interstorey isolation as a non-conventional TMD and introduced a method for the seismic design of such a system, whereas in [6], a 3-DOF model was used to investigate the dynamic and seismic benefits of an intermediate discontinuity for a general frame structure.

The present paper assesses the improvement of the behavior of a frame structure due to the coupling with an external structure shorter than the frame structure and connected only to the first storey, so it has a limited visual impact. The purpose of this study is to understand if the connection with the external structure can reduce both the displacement of the connected storey (i.e., the first storey of the structure) and the drift of the structure above the connection, without changing the geometrical and the mechanical properties of the frame structure to protect. The connection between the frame and the external structures is performed with visco-elastic device. A general multi-storey frame is described with a 2-DOF model, whereas a 1-DOF model is used to describe the external structure.  Moreover, an inerter device is applied to the external structure to modify its inertial force. The coupled structure is described by a 3-DOF linear elastic mechanical model. The coupling with the external structure is considered beneficial for the frame when there is a reduction in the displacements and drifts of the coupled structure with respect to the stand-alone frame structure.

The effects of the coupling with the external structure and with the inerter device are shown in terms of modification of the frequencies and modal shapes. It is observed that, if the mechanical characteristics of the coupling system are suitably chosen, the first mode of the coupled system maximizes the modal displacement of the external structure and minimizes the modal displacements of the frame structure. Moreover, this mode acquires a modal mass participating factor that overcomes the 90%, thus making the dynamics of the system very regular.

Further parametric analysis is performed exciting the coupled structure with several ground motion records. The results are arranged in performance maps that compare the displacements and drifts of the coupled structure with those of the stand-alone frame structure.  Each map is built by varying the stiffness of the external structure and the connection device, for fixed values of the other characteristics of the coupled structure. It is found that there are wide regions in the plane of the parameter where the coupling is beneficial for the frame structure. In correspondence with the points of the maps where the highest reduction in displacements or drifts occur, the external structure work similarly to a tuned mass damper.

References

[1] J. Kelly. Base isolation: linear theory and design. Earthquake Spectra, 6(2):223{244, 1995.

[2] J.-P. Den Hartog. Mechanical vibrations, 4th edn. McGraw-Hill, New York, 1956.

[3] J.A. Bachmann, M.F. Vassiliou, and B. Stojadinovi. Dynamics of rocking podium structures. Earthquake Engineering and Structural Dynamics, 46(14):2499{2517, 2017. Dynamics, 47(15):2965{2984, 2018.

[4]  A. Di Egidio, S. Pagliaro, and C. Fabrizio. Combined use of rocking wall and inerters to improve the seismic response of frame structures. Journal of Engineering Mechanics, 147(5), 2021.

[5]  A. Reggio and M. De Angelis. Optimal energy based seismic design of nonconventional Tuned Mass Damper (TMD) implemented via interstory isolation. Earthquake Engineering and Structural Dynamics, 44(10):1623{1642, 2015.

[6] S. Pagliaro and A. Di Egidio. Archetype dynamically equivalent 3-d.o.f. model to evaluate seismic performances of intermediate discontinuity in frame structures. Journal of Engineering Mechanics, 148(3), 2022.