Stick motions and grazing flows in an inclined impact oscillator |
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| Institution: | 1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China;3. Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom;1. Department of Mechanics, Beijing Institute of Technology, Beijing 100081, People''s Republic of China;2. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, People''s Republic of China |
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| Abstract: | In this paper, the dynamics of an inclined impact oscillator under periodic excitation are investigated using the flow switchability theory of the discontinuous dynamical systems. Different domains and boundaries for such system are defined according to the impact discontinuity. Based on above domains and boundaries, the analytical conditions of the stick motions and grazing motions for the inclined impact oscillator are obtained mathematically, from which it can be seen that such oscillator has more complicated and rich dynamical behaviors. The numerical simulations are given to illustrate the analytical results of complex motions, and several period-1 motions period-2 motion and chaotic motion of the ball in the inclined impact oscillator are also presented. There are more theories about such impact pair to be discussed in future. |
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