| In mechanical engineering field, there are two common and important contact-s between two dynamical systems, i.e., impact and friction. In order to improve energy efficiency, discontinuous models in mechanical engineering should be ana-lyzed and accurately predicted. So some new theories on discontinuous systems-discontinuous dynamical systems- have been proposed to investigate discontinuous model. By using discontinuous dynamical systems theories, this paper mainly in-vestigated the discontinuous dynamics of a non-linear, periodically forced inclined impact oscillator with dry-friction. This paper is divided into three chapters.In Chapter 1, we introduce the research background and research significance of discontinuous dynamical systems, and give the theory and concept of discontinuous dynamic system on dynamic domain.In Chapter 2, we investigate the discontinuous dynamics behavior of a non-linear, periodically forced inclined impact oscillator with dry-friction. From the Newton's law, the momentum conservation and the simple impact law, motion e-quations can be obtained. Different domains and boundaries for such system are defined according to the dry-friction and the impacting discontinuity. To under-stand the motion switchability, the analytical conditions for motion switchability at the discontinuous boundaries in such periodically forced inclined impact oscilla-tor with dry-friction are developed by using the the flow switchability theory for the discontinuous dynamical systems. Switching sets and basic mappings are de-fined through discontinuous boundaries. Analytical predictions for periodic motions are developed by using mapping structures. Based on such analytical conditions for motion switching, numerical simulations are given to illustrate the analytical results of the complex motions.In Chapter 3, we summarize the main contents of this paper, and prospect some new problems and theories that can be studied future. |
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