Calculation of the dynamic responses of a dry-friction oscillator under harmonic excitation

In this paper, an analytical method is presented to calculate the dynamic responses of a harmonic forced oscillator with dry friction. The friction of the oscillator is modeled by an Iwan model with finite Jenkins elements. As the force-displacement relationship of the oscillator is piecewise linear, the motion of the oscillator is analyzed interval by interval. The vibration equation in each linear interval is given and the corresponding analytical solution is derived by use of variable substitution. The initial values of each interval are obtained by the continuity condition of the displacement and velocity of the oscillator. Combining the dynamic responses of these intervals in sequence forms the dynamic responses of the model in the whole time history. The simulation results show that as the excitation amplitude level increases, slipping occurs in the contact surface which makes the contact stiffness decreased, thus results in obviously left shifted of the peak amplitude of the frequency response function curves. It is also found that the equivalent viscous damping first increases then decreases with the excitation amplitude level.