Observation and investigation of a non-monotonic period function for an impact oscillator |
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| Authors: | Carmen Chicone Kenny Felts Brian Mann |
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| Affiliation: | 1. Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211-4100, United States;2. Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, United States;1. Department of Mathematical Sciences, The University of South Dakota, Vermillion, USA;2. Grupo de Ecología Matemática, Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Chile;1. Politechnika ?wi?tokrzyska, Al. 1000-lecia PP 7, 25-314 Kielce, Poland;2. Collegium Mazovia, ul. Soko?owska 161, 08-110 Siedlce, Poland;1. College of Mechanical Engineering, Chongqing University, Chongqing 400044, China;2. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China;3. School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China;4. College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China;1. Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK;2. School of Life Sciences, University Park, Nottingham NG7 2RD, UK;3. Vetinary Academic Building, Sutton Bonington Campus, University of Nottingham, Sutton Bonington, Leicestershire LE12 5RD, UK |
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| Abstract: | A mathematical model for a bench-top impact oscillator (a steel pendulum and an aluminum barrier) that incorporates Hertzian contact is analyzed, and predictions derived from our model are compared with experimental data. We report our discovery of a new effect: the existence of a non-monotone period function for the annulus of periodic orbits in the phase plane surrounding the rest point that corresponds to the downward vertical position of the pendulum in the unforced, undamped case. From this non-monotonicity, we predict novel resonance response behavior for the forced, damped oscillator and verify our predictions by experiment. |
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