Exact solutions of the problem of the vibro-impact oscillations of a discrete system with two degrees of freedom |
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| Institution: | 1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China;2. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710062, China;3. Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt;4. Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt;1. Infineon Technologies AG, Am Campeon 1-15, 85579 Neubiberg, Germany;2. Fraunhofer Institute for Electronic Nanosystems ENAS, Technologie-Campus 3, 09126 Chemnitz, Germany;3. Technische Universität Chemnitz, Center for Micro-Technologies, Reichenhainer Straße 70, 09126 Chemnitz, Germany |
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| Abstract: | 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. |
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