Seismic Benefits from Coupling Frame Structures with a Hysteretic Mass Damper Inerter

The coupling of frame structures with external oscillating bodies, such as rigid walls, dynamic mass absorbers, elastoplastic dampers, or tuned mass dampers, can be effective in reducing the displacements of the structure and protecting it against seismic loads. This paper proposes connecting an external oscillating body to the first story of a frame structure and studying the effectiveness of the coupling by evaluating the reduction in the displacements of the frame structure. The inertial effects of the oscillating body are increased by introducing a virtual mass, provided by an inerter device. The oscillating body, characterized by physical and virtual masses, is connected to the frame structure through a hysteretic device. The study is performed on a dynamically equivalent three-degree-of-freedom (3-DOF) model, whose equations are written using a direct approach. To verify the effectiveness of the protection device, named hysteretic mass damper inerter (HMDI), in reducing the displacements of the frame structure, the displacement of the first story and the drifts of the upper stories are compared to those of the frame structure not connected to the external oscillating body. An initial spectral analysis, performed on the linearized mechanical system, clarifies the role of the parameters of the external device in the dynamic behavior of the coupled system. An additional seismic analysis is performed by using three single earthquake records first, and then a set of seven additional earthquake records selected to be compatible with the design spectrum of Los Angeles. Specific spectral gain maps are used to organize the results of an extensive parametric analysis. They show that the HMDI reduces both displacements and drifts of the structure in large ranges of the parameters that characterize the HMDI. It is found that the proposed protection method is particularly effective for low- and medium-rise frame structures.