Can friction damping be accurately modeled with massless bilinear hysteresis elements? This study examines the performance of these elements in dynamic systems, commonly used to model frictional energy dissipation. These quasi-static elements use damper stiffness and slip force as parameters, making them highly relevant in the field of **physics** and the design of mechanical systems. While bilinear hysteresis elements capture the qualitative nature of friction-damped forced response, quantitative comparisons often present difficulties. This paper explores the role of damper mass in energy dissipation, evaluating its influence on the kinematic state of the damper (pure slip, stick-slip, pure stick). Differences between massless and non-zero mass cases are also examined. Ultimately, this paper develops transition maps describing damper response kinematics in damper parameter space, delineating linear analysis regions (pure slip, pure stick) from nonlinear regions (stick-slip). The results reveal that even small damper mass can significantly impact system response and provide advantages over the massless case, which is crucial for effective **engineering** and control, particularly in systems experiencing vibration.
Published in the Journal of Vibration and Acoustics, this study aligns with the journal’s focus on understanding and modeling dynamic systems involving vibration and energy dissipation. By exploring the performance of bilinear hysteresis elements in representing friction damping, it contributes to the field of vibration analysis and control. The references demonstrate engagement with relevant research in mechanical engineering, dynamics, and tribology.