Wake-induced response of vibro-impacting systems

The effects of a rigid barrier on the stability of the structure while it is undergoing phase-locked motions due to the surrounding fluid–structure interactions, are studied. The primary structure and the near wake dynamics are modeled as a harmonic oscillator and a Van der Pol oscillator, respectively, and are weakly coupled via acceleration coupling. Qualitative changes in the dynamical behavior of this system are investigated in the context of discontinuity-induced bifurcations that result from the interaction of fluid flow and nonsmoothness from the impact of the primary structure. Phenomenological behaviors like the co-existence of attractors and period-adding cascades of limit cycles separated by chaotic orbits are observed. The behavior of orbits in the local neighborhood of the discontinuity boundary is defined using a higher-order transverse discontinuity map, and the corresponding stability analysis is carried out using Floquet theory. The derived mapping is implemented to obtain the respective Lyapunov exponents. Results obtained using the mapping are demonstrated to accurately predict both the stable and chaotic regimes, as observed from the corresponding numerical bifurcation diagrams.