Uncertainty propagation for nonlinear vibrations: A non-intrusive approach

Abstract

The propagation of uncertain input parameters in a linear dynamic analysis is reasonably well established today, but with the focus of the dynamic analysis shifting towards nonlinear systems, new approaches is required to compute the uncertain nonlinear responses.A combination of stochastic methods (Polynomial Chaos Expansion, PCE) with an Asymptotic Numerical Method (ANM) for the solution of the nonlinear dynamic systems is presented to predict the propagation of random input uncertainties and assess their influence on the nonlinear vibrational behaviour of a system. The proposed method allows the computation of stochastic resonance frequencies and peak amplitudes based on multiple input uncertainties, leading to a series of uncertain nonlinear dynamic responses. One of the main challenges when using the PCE is thereby the Gibbs phenomenon, which can heavily impact the resulting stochastic nonlinear response by introducing spurious oscillations. A novel technique to avoid the Gibbs phenomenon is be presented in this paper, leading to high quality frequency response predictions.A comparison of the proposed stochastic nonlinear analysis technique to traditional Monte Carlo simulations, demonstrates comparable accuracy at a significantly reduced computational cost, thereby validating the proposed approach.