On Friction Damping Modeling Using Bilinear Hysteresis Elements

Massless bilinear hysteresis elements are often used to model frictional energy dissipation in dynamic systems. These quasi-static elements possess only two describing parameters, the damper stiffness and the force at which it slips. Bilinear hysteresis elements capture the qualitative nature of friction-damped forced response, but sometimes have difficulty with quantitative comparisons. This paper examines the performance of massless bilinear hysteresis elements as well as the role of damper mass in energy dissipation, and specifically evaluates its influence on the kinematic state of the damper (pure slip, stick-slip, pure stick). Differences between the massless and non-zero mass case are explored, as are the implications on both damper and system response. The results indicate that even small damper mass can have a qualitative effect on the system response, and provide advantages over the massless case. Further, we develop transition maps, describing damper response kinematics in the damper parameter space, which segment the space into two linear analysis regions (pure slip, pure stick) and one nonlinear analysis region (stick-slip). The results suggest non-zero mass dampers which are tuned as optimal vibration absorbers provide substantial resonance response attenuation and substantially reduce the size of the nonlinear analysis region in the damper parameter space.