Periodic Solutions, Bifurcations, Chaos and Vibration Quenching in Impact Damper

Abstract

This paper deals with a two-degree-of-freedom forced system composed of a main system and an impact damper which has been analyzed by many researchers. Periodic solutions, bifurcations, chaos, and vibration quenching are discussed. A shooting method for impact systems presented by authors is used in numerical calculations. The following results were obtained : (1) Unsynmetric periodic solution with four collisions per period and subharmonic vibrations with many collisions were found. (2) Discontinuities in the stability of the periodic solutions caused by impact were shown using characteristic multipliers. (3) Two routes to chaos were found, namely, the period doubling route and the torus doubling route. (4) Hyper chaos was found for the first time in the impact damper system. (5) The vibration quenching problems for the narrow frequency region near the resonance point and for the wide frequency region were discussed.

On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink

“…Another phenomenon is about possible types of the bifurcation and route to chaos during sweep experiments (e.g. observed in [27]). All possible cases can be explained clearly.…”

“…The research of impact damper has been around two main themes. The first one is about the dynamics: response regimes and stability by analytical study in [22] and with experimental validation in [23,24], bifurcation and chaos by numerical study with the combination use of time series, phase trajectories, bifurcation diagrams [25], Poincare maps [26] and Lyapunov exponential [27]. Similar study has been carried out for the impact oscillator by Pekerta [28].…”