Modelling elastic structures with strong nonlinearities with application to stick–slip friction

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Abstract

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low-dimensional equation with memory. The method is general and well suited to problems with isolated discontinuities such as friction and impact at point contact. It is assumed that the structure is composed of two parts: a continuum but linear structure and finitely many discrete but strong nonlinearities acting at various contact points of the elastic structure. The localized nonlinearities include discontinuities, e.g. the Coulomb friction law. Despite the discontinuities in the model, we demonstrate that contact forces are Lipschitz continuous in time at the onset of sticking for certain classes of structures. The general formalism is illustrated for a continuum elastic body coupled to a Coulomb-like friction model.
Original languageEnglish
Article number20130593
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume470
Early online date20 Nov 2013
DOIs
Publication statusPublished - 8 Jan 2014

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