Suggestion of an equation of motion to calculate the damping ratio during earthquake based on a cyclic procedure

Abstract

Large horizontal relative displacements are naturally caused by seismic excitation, which is able to provide collisions between two adjacent buildings due to insufficient separation distance and severe damages due to impacts, especially in tall buildings. In this paper, the impact is numerically simulated and two needed parameters are calculated, including the impact force and energy absorption. In order to calculate the mentioned parameters, mathematical study is carried out to model an unreal link element, which is logically assumed to be a spring and dashpot to determine the lateral displacement and damping ratio of the impact. For the determination of the dynamic response of the impact, a new equation of motion is theoretically suggested to the evaluate impact force and energy dissipation. In order to confirm the rendered equation, a series of parametric studies are performed and the accuracy of the formulas is confirmed.