Vibro-impact nonlinear energy sink dynamics in a harmonically excited weakly coupled two-degree-of-freedom linear oscillator

This paper presents a comprehensive study of periodically forced, weakly coupled two-degree-of-freedom (2-DOF) linear oscillators integrated with a vibro-impact nonlinear energy sink (VI NES).The system under consideration features a slowly varying main linear oscillator with repeated resonance frequencies. Utilizing Slow Invariant Manifold (SIM) analysis and the multiple-scale method, an asymptotic analytical framework is developed to investigate the system dynamics near the 1:1 resonance region. Six distinct response regimes of the system are identified and analyzed through both numerical simulations and analytical predictions. The results reveal excellent agreement between numerical and analytical findings across multiple regions. Furthermore, in contrast to single-degree-of-freedom (SDOF) main linear systems, a novel response regime—quasi-periodic response—and the coexistence of multiple solutions are reported and investigated for the first time in this system. Additionally, the influence of clearance on the maximum amplitude and vibration suppression performance of the main linear oscillators is examined under constant frequency conditions. The findings indicate distinct response regimes for the two linear oscillators under optimal clearance conditions. Finally, a sweep-frequency analysis is conducted to determine the optimal parameters of the VI NES system across the entire resonance frequency band.