The effect of friction on the dynamics of targeted energy transfer by symmetric vibro-impact dampers

Abstract: This study investigates the nonlinear dynamics of a symmetric vibro-impact nonlinear energy sink (VI-NES) subjected to dry friction, a crucial factor that remains insufficiently explored in previous research. The combined effect of impact and friction leads to intricate behaviors that require further investigation. To address this, the multiple scales method is extended to incorporate frictional effects and is complemented with a generalized impact map approach. This allows for a systematic exploration of periodic solutions, stability, and bifurcations, revealing critical transitions between impact-dominated and sliding-dominated regimes. The activation thresholds and amplitude levels for different response regimes, including stick-slip dynamics, are identified, offering new insights into friction-induced nonlinearities. The results bridge the gap between theoretical modeling and practical implementation, offering a more accurate predictive framework for VINES behavior. This improves design strategies for enhanced energy dissipation and robustness in real-world applications.