Most engineering structures, for example airplane landing gear, jet engines and gearboxes, involve friction and impact among their components. Traditionally these harsh phenomena are difficult to design for and introduce a great deal of uncertainty in the final product.
The new research offers an alternative view on this problem by providing a modelling technique that allows for more accurate predictions than methods currently available. The proposed method also offers a better understanding of contact mechanics, which might be used to achieve a better design.
Dr Róbert Szalai, Lecturer in the Department of Engineering Mathematics, said: “One of the greatest concerns of engineers is modelling friction and impact.
“Building prototypes to test engineering structures can be extremely expensive and this new modelling technique could mean a prototype does not need to be built.”
Alan Champneys, Professor of Applied Non-linear Mathematics in the Department of Engineering Mathematics, added: “Strongly nonlinear behaviour, such as stick-slip motion and impact, are a huge cause of uncertainty in engineering systems.
“The findings from this paper provide a key breakthrough in research that is being pursued by a consortium of major universities and industrialists to address these problems as part of an EPSRC programme grant.”
In the paper, the researcher has presented a general mechanical model and described a model reduction technique. The new model includes a memory term to account for effects that traditional models ignore. The study has also discussed the convergence of the method and its implications to non-smooth systems.
The derivation of the memory term is illustrated through the examples of a pre-tensed string and a cantilever beam. The paper has used the example of a bowed string and has demonstrated the properties of the transformed equation of motion, in particular its convergence as the number of vibration modes goes to infinity.
Paper: Modelling elastic structures with strong nonlinearities with application to stick–slip friction, Róbert Szalai, Proceedings of the Royal Society A, 20 November 2013.