A non-intrusive frequency normalisation approach for uncertain response analysis of nonlinear dynamic systems

This paper proposes a non-intrusive technique based on the frequency normalisation for non-intrusive propagations of parameter uncertainties in nonlinear mechanical systems. The multi-solution dilemma found in resonance areas, which prohibits successful applications of uncertainty quantification methods, is alleviated by the additional normalised frequency measure. The spurious peaks around the nonlinear peaks and discontinuous points, known as the Gibbs phenomenon, due to parameter variabilities are resolved as well. The proposed technique coupled with the non-intrusive surrogate modelling is applied to two deliberately constructed nonlinear dynamic systems, i.e., a mass-spring system with interactive cubic nonlinearity and a piece-wise rotor/stator contact problem in rotating machines. The two systems exhibit complex amplitude-frequency response characteristics featured by the softening and hardening effects. Numerous case investigations show the effectiveness of the proposed normalisation method for uncertainty analysis of complex nonlinear vibration systems and its working principle is demonstrated in detail via examples. Accuracy tests against the traditional sampling methods are carried out in both systems. The proposed technique can be easily generalised to other nonlinear systems for random and non-random uncertainty propagations because it works non-intrusively and permits users to choose arbitrary nonlinear tools.