Exact solutions of the problem of the vibro-impact oscillations of a discrete system with two degrees of freedom

Non-smooth time transformations are used to investigate strongly non-linear periodic free oscillations of a vibro-impact system with two degrees of freedom. Allowance for the boundary conditions at collision times enables the singularities induced by these transformations to be eliminated. The smoothed equations of motion turn out to be linear. Investigation of the periodic solutions reveals vibro-impact states with one- an two-sided collisions, including localized states (only one of the masses experiences collisions with stopping devices), and their bifurcation structure. (C) 1999 Elsevier Science Ltd. All rights reserved.