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A hybrid scheme for simulation of planar rigid bodies with impacts and friction using impact mappings |
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| Institution: | 1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain;2. Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal;1. University of Cagliari, DICAAR—Department of Civil and Environmental Engineering and Architecture, via Marengo, 2, I-09123 Cagliari, Italy;2. Intes GmbH, Schulze-Delitzsch-Straße 16, D-70565 Stuttgart, Germany;3. Technische Universität Dresden, Institut Statik und Dynamik der Tragwerke, Schumann-Straße 10, D-01062 Dresden, Germany;4. University of Sassari, DADU—Department of Architecture, Design and Urban Planning, Asilo Sella, via Garibaldi, 35, I-07041 Alghero (SS), Italy;1. A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharskoho St., 61046 Kharkiv, Ukraine;2. 377 H Administration Building, MC-348, 506 South Wright Street, Urbana, IL 61801, USA |
| Abstract: | This paper introduces numerical techniques necessary for the implementation of impact maps derived from an energetic impact law for rigid-body impacts with friction at isolated contact points. In particular the work focuses on methodologies for long-term simulation with behaviours such as dynamic transitions and chatter. The methods are based on hybrid event-driven numerical solvers for ordinary differential equations together with system states to deal with the transitions. A slender rod impacting a periodically oscillating surface is used as an example to illustrate implementation and methods. The numerical scheme for the rod system is used to show how symmetry can play an important role in the presence of friction for long-term dynamics. This will show that surface oscillations with low frequencies tend to lead to periodic motions of the rod that are independent of friction. For higher frequencies however the periodic solutions are not that common and irregular motion ensues. |
| Keywords: | Rigid body mechanics Hybrid event driven method Coulomb friction Impact Non-smooth Bifurcation |
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