Periodic motions of coupled impact oscillators

International audienceIn this work, we study the existence and stability of time-periodic oscillations in a chain of linearly coupled impact oscillators reminiscent of a model analyzed in [2], for rigid impacts without energy dissipation. We introduce a numerical method allowing to compute branches of time-periodic so- lutions when an arbitrary number of nodes undergo rigid impacts. For this purpose, we reformulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. We illustrate this numerical approach by computing some families of nonlinear spatially localized modes (breathers) and extended modes