Proposing an analytical relationship to calculate the damping inclination of rigid single mass impact dampers

In high amplitude vibrations when there is an impact damper, effective collisions occur between the damper particle and the main structure. These effective collisions cause the energy of the main system decreases significantly. The use of impact dampers in the free vibrations of a system of one degree of freedom reduces the amplitude of vibrations linearly, where the slope of this line is called the damping inclination.The damping inclination is a criterion of the damper performance, whose number indicates the effect of using the impact damper in reducing the vibrations of the oscillating system. In most of the previous researches, the damping inclination has been extracted by numerical or experimental methods, and no formula has been presented to predict the damping inclination. In this research, the effect of parameters of the coefficient of restitution and the mass ratio on the damping inclination of rigid single mass impact dampers has been studied. Then, by analyzing the data, an analytical relationship has been presented to determine the damping inclination according to the coefficient of restitution and mass ratio. This formula predicts the damping inclination with an error of less than six percent and eliminates the need for numerical and experimental studies to determine the damping inclination.