A new modelling technique has been developed that could eliminate the need to build costly 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 Proceedings of the Royal Society A.

Most engineering structures, for example airplane landing gear, jet engines and gearboxes（变速箱）, involve friction（摩擦力） 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（收敛，集合） 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.