Resonances in linear one-degree-of-freedom systems with piecewise-constant parameters |
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| Institution: | 1. Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia 20650, Morocco;2. Department of Mathematics, FSTE Moulay Ismail University of Meknes, BP 509 Boutalamine, Errachidia 52000, Morocco;3. Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey;1. Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, Ministry of Education, China University of Mining and Technology, Xuzhou 221008, China;2. School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China;3. Geological Research Institute for Coal Green Mining, Xi''an University of Science and Technology, Xi''an 710054, China;4. College of Geology and Environment, Xi''an University of Science and Technology, Xi''an 710054, China |
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| Abstract: | A technique based on the composition of elementary phase fluxes is proposed for investigating parametric resonance in systems with “large” perturbations, described by second-order linear differential equations with periodic piecewise-constant coefficients. A monodromy matrix is given and a parametric resonance criterion is indicated, which takes into account the possibility of multiple multipliers and the action of dissipative forces. When there is a two-stage dependence of the coefficients on time during one period, regions of parametric resonance are obtained for different types of linear mechanical systems with one degree of freedom. |
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