Wake-induced response of vibro-impacting systems

The stability and bifurcation behaviour of a wake-induced vibro-impacting oscillator is studied. The effects of a discontinuity on the stability of the structure while it is undergoing phase-locked motions due to the surrounding fluid-structure interactions (FSI) are examined. The primary structure and the near wake dynamics are modelled as a harmonic oscillator and a Van der Pol oscillator, respectively, and are weakly coupled to each other via acceleration coupling. Qualitative changes in the dynamical behaviour of this system are investigated in the context of discontinuity-induced bifurcations (DIBs) that result from the interaction of fluid flow and non-smoothness from the primary structure. Phenomenological behaviours like the co-existence of attractors and period-adding cascades of limit cycles separated by chaotic orbits are observed. The existence of these phenomena is demonstrated via stability analysis using Floquet theory and the associated Lyapunov spectra. In addition, the behaviour of orbits in the local neighbourhood of the barrier is defined using a higher-order transverse discontinuity map. This mapping is implemented to obtain the respective Lyapunov exponents. Solutions obtained using this modified algorithm are demonstrated to accurately predict both stable and chaotic regimes, as observed from the corresponding bifurcation diagrams.