Semi-Analytical Periodic Motions in Impact Duffing Oscillator

Abstract In this paper, impact periodic motions in a periodically forced Duffing oscillator with one-side wall are obtained semi-analytically through implicit mappings. The implicit mapping is determined through the discretization of the impact Duffing oscillator. The mapping structures are employed to construct specific impact periodic motions for an impact Duffing oscillator. The impact periodic motions are presented for a better understanding of discontinuous dynamical systems and the grazing impact motions are obtained for impacts adding of impact periodic motions.