  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.
