Balkis Youssef

Zusammenfassung

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 VI-NES behavior. This improves design strategies for enhanced energy dissipation and robustness in real-world applications.

Zusammenfassung

This paper examines the dynamics of a vibro-impact nonlinear energy sink (VI-NES) using a generalized impact map approach. The study incorporates asymmetry and dry friction, reflecting realistic conditions. The proposed method identifies all periodic solutions and determines their stability, and is applicable to various VI-NES configurations, including horizontal and vertical orientations. Numerical results validate prior findings for symmetric frictionless cases and extend them to include frictional and asymmetric dynamics, providing a powerful tool for optimizing the performance of VI-NES in vibration mitigation.

Zusammenfassung

The aim of the paper is to formulate a complete set of design rules for a vibro-impact nonlinear energy sink (VI NES). Hereto, analytical and numerical methods to extract the backbone curve of vibro-impact systems are presented. The adopted approach exploits the multiple scales method and is applied to a linear oscillator coupled with a VI NES. The dynamics of the system are explored and the system’s response under harmonic forcing in the vicinity of resonance is analyzed and approximated. The presented method allows for the derivation of a closed-form approximation of a nonlinear mode. The relation between the steady state response and the input parameters is established. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical predictions are confirmed through a comparison with the standard resonant decay method combined with a phase-locked loop. Finally, the closed-form approximations are used to derive a complete set of design rules for a vibro-impact nonlinear energy sink.