FIRST RETURN TIME TO THE CONTACT HYPERPLANE FOR N-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEMS

The paper deals with the dynamics of conservative N-degree-of-freedom vibro-impact systems involving one unilateral contact condition and a linear free flow. Among all possible trajectories, grazing orbits exhibit a contact occurrence with vanishing incoming velocity which generates mathe-matical difficulties. Such problems are commonly tackled through the defini-tion of a Poincare ' section and the attendant First Return Map. It is known that the First Return Time to the Poincare ' section features a square-root sin-gularity near grazing. In this work, a non-orthodox yet natural and intrinsic Poincare ' section is chosen to revisit the square-root singularity. It is based on the unilateral condition but is not transverse to the grazing orbits. A detailed investigation of the proposed Poincare ' section is provided. Higher-order sin-gularities in the First Return Time are exhibited. Also, activation coefficients of the square-root singularity for the First Return Map are defined. For the linear and periodic grazing orbits from which bifurcate nonlinear modes, one of these coefficients is necessarily non-vanishing. The present work is a step towards the stability analysis of grazing orbits, which still stands as an open problem.