# Seismic Benefits from Coupling Frame Structures with a Hysteretic Mass Damper Inerter  
[PERSON]  
1 Department of Civil, Construction-Architectural and Environmental Engineering, University of L'Aquila, 67100 L'Aquila, Italy 1t1 Department of Civil, Construction-Architectural and Environmental Engineering, University of L'Aquilaliterature propose similar approaches based on low-dimensional models. For example, 2-DOF models were used to study the advantages of base isolation in [1] and the effectiveness of the protection through tuned mass dampers (TMD) in [2; 3; 4]. Similarly, in [5; 6], 2-DOF models were used to investigate the ability of a TMD to reduce the base displacement of a base-isolated system. Moreover, in [7; 8], the behavior of a structure placed on a rocking medium is investigated using low-dimensional models. Additionally, in [9; 10; 11; 12], archetype models were used to analyze the seismic performances of coupling a frame structure with an external rocking wall. More recently, the effectiveness of coupling a frame structure with external systems equipped with inerter devices and a yielding exoskeleton was studied in [13; 14], respectively. Low-dimensional models were also used to describe the dynamics of rigid body-like structures, as in [15; 16], where different active control algorithms were considered to improve the seismic performance of such structures. The seismic effectiveness of an intermediate discontinuity in a frame structure was studied in [17; 18] by using a 2-DOF mechanical model; in [19; 20], the authors performed analytical and experimental investigations on frame structures with inter-story isolation by using a 3-DOF model. The idea behind the protection device studied in this paper is derived from studies of protection systems based on TMDs connected with structures to protect by viscoelastic devices. To ensure the effectiveness of a TMD, a small mass is usually sufficient. However, in the case of seismic excitation, the use of a small mass may undermine the effectiveness of the TMD. This issue can be addressed by coupling the TMD with an inerter device that increases its inertial forces, as described in [21]. Inerter devices and their applications, mostly related to the control of engineering structures, have been studied for about two decades and, at the state-of-the-art, several types of inerter devices and relative models have been proposed [22] and experimentally tested [23; 24; 25]. Some studies fully characterized the nonlinear behavior of the inerter device that may play a significant role in some applications, such as the one proposed in this paper. The device obtained by coupling a TMD with an inerter device, named tuned mass damper inerter (TMDI), was investigated in several papers [26; 27; 28; 29; 30; 31], some of which specifically focused on increasing the efficiency of base isolation [32]. Moreover, in the case of TMDIs, several studies were carried out on archetype or simplified models with a limited number of DOFs [33]. Following a similar approach, this paper investigates the possible improvement of the dynamic behavior of a frame structure by coupling it with an external oscillating body linked to the first story of the frame structure through a hysteretic coupling device. Moreover, in this case, the inertial effects of the oscillating body are increased by using an inerter device. Such a protection device, which comprises the oscillating body, the connection device, and the inerter device, is called a hysteretic mass damper inerter (HMDI), similar to the TMDI, and has already been used in [34] for the protection of rigid block-like structures against seismic excitation. The purpose of this study is to understand if the HMDI can reduce the displacement of the first story and the drifts of the upper stories without modifying the properties of the frame structure to protect. The coupled structure (i.e., the structure plus the protection device) is modeled by a 3-DOF analytical model described by equations of motion written using a direct approach.