Analytical Method for Designing the Tuned Mass Damper Based on the Complex Stiffness Theory

摘要

In this paper, a new approach is presented for designing the tuned mass damper (TMD). Formulation of the dynamic magnification factor for the absorbed structure leads to a nonlinear equation, which is solved here analytically for determining the TMD's specifications. Suitable root, selected based on the structural dynamic theories, is complex, which shows that the TMD mechanism probably has little damping. This formulation leads to new closed-form relationships for designing the TMD's mass, stiffness and damping. For numerical verification of the proposed method, vibrations of two shear buildings, excited by some near-field and far-field ground acceleration records, are controlled using the TMD mechanism. Results show that the efficiency of the proposed technique for controlling the structural vibrations is higher than other existing approaches.