Anti-optimisation for modelling the vibration of locally nonlinear structures: An exploratory study

Modelling the vibration of complex structures with uncertain nonlinearities is a significant challenge. However, nonlinearities are often spatially localised: this enables efficient linear methods to describe the behaviour of the majority of the structure and reduces the size of the nonlinear problem. This paper explores anti-optimisation as an approach to modelling uncertain nonlinearities for this class of system. The 'worst-case' output metric is sought by considering nonlinear forces as an external input subject to constraints that capture what is known about the nonlinearity. A systematic sequence of tests is carried out using a mass on spring system within a pair of end-stops: the results show how the anti-optimised solutions become less conservative as the constraints are increasingly restrictive. The method is applied to bending vibration of a beam within a pair of local end-stops. Anti-optimised solutions are found as a function of frequency and are compared with a Monte Carlo set of benchmark simulations. Almost all anti-optimised solutions over-predict the simulations and the overall trend of the simulations is also clearly captured. The method shows significant potential and motivates further research.