Lyapunov exponents in discrete modelling of a cantilever beam impacting on a moving base |
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| Institution: | 1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China;2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China;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 |
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| Abstract: | The dynamic behaviour of a cantilever beam of an unnegligible large mass and with a concentrated mass fixed at its end, which impacts on a movable base according to Hertz's damp law, is studied. A new finite element reference model of the system and its lower-dimensional substitutive models with one degree or two degrees of freedom are developed. The qualitative-type as well as quantitative-type applicability limits of these substitutive models are discussed - the latter ones are described in terms of the corresponding spectra of Lyapunov exponents. |
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| Keywords: | Impacting cantilever beam Hertz's damp contact model Periodic solution Lyapunov exponents |
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