Design of a Dynamic Absorber for a Vibrating Frame with Three Degrees of Freedom

The study of the mechanical vibrations of a system is important to ensure the safety of a structure. In the field of civil engineering, it is becoming increasingly common to use auxiliary systems called dynamic absorbers, also called Tuned Mass Dampers (TMDs), which are capable of decreasing the vibrations of the main system. They are characterized by mass-spring systems and eventually by a damper. In virtue of the presence of such systems, the operating frequency band of the main structure can be expanded. They are used in civil engineering works to counteract both the action of earthquakes, which cause excitation at the base of the structure, and wind action, which must be taken into account especially in the case of high-rise buildings. In this paper, we will focus on the optimal design of the parameters of a TMD for a vibrating frame with three degrees of freedom. The purpose of this paper is to demonstrate that the Den Hartog method can be generalized for a Multiple Degrees of Freedom (MDF) system. To this end, we will consider the structure subjected to a displacement imposed at the base by an earthquake that occurred in Loma Pietra in 1989. The dynamic analysis of the system was carried out by using MATLAB, while for the realization of the virtual 3D structure we used INVENTOR.