A new modelling technique has been developed that could eliminate the need to build costly¹ prototypes（原型）, which are used to test engineering structures such as aeroplanes. The study, by Dr Róbert Szalai at the University of Bristol, is published in the latest issue of the Proceedings² of the Royal Society A.

 

Most engineering structures, for example airplane landing gear, jet engines and gearboxes（变速箱）, involve friction³（摩擦力） and impact among their components⁴. Traditionally these harsh phenomena⁵ are difficult to design for and introduce a great deal of uncertainty⁶ 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 Applied⁷ 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 industrialists⁸ 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（收敛，集合） of the method and its implications to non-smooth systems.

 

The derivation of the memory term is illustrated⁹ through the examples of a pre-tensed string and a cantilever¹⁰ 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 vibration¹¹ modes goes to infinity¹².

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