My research aims to find efficient and practical ways of predicting the vibration response of complex structures with spatially localised nonlinearities. Often these nonlinearities are poorly characterised, so the aim is to develop methods that can include the effect of uncertainties. Application areas of particular interest include: brake systems with a local nonlinear frictional contact; oilwell drills with localised interactions with the borehole wall; and turbine blades in contact with their casing structure