Non-intrusive Frequency Response Analysis of Nonlinear Systems with Interval Uncertainty: A Comparative Study

This paper investigates the non-intrusive frequency response function (FRF) computation of nonlinear vibration systems subject to interval uncertainty. The arc-length ratio (ALR) method is generalized into non-probabilistic nonlinear problems and the interpolation technique is introduced to adapt the ALR for classic predictor-corrector algorithms. The ALR method is comparatively studied with the polar angle interpolation (PAI), which is another state-of-the-art technique for uncertainty propagation in nonlinear FRFs. Applications of the two techniques to two nonlinear systems, i.e., a dual-rotor with rotor/stator contact and a two degrees-of-freedom system with cubic nonlinearity, are presented. The in-depth case studies reveal the essence of the two methods and their strengths and limitations. It is found that the ALR is a powerful tool for various problems while the PAI may fail in nonlinear systems whose FRFs have extreme curvatures or complex shape structures. However, the PAI can transform the uncertain FRF bands into a traditional frequency sense. As the uncertainty propagation methods constructed in the present study are non-intrusive, they can be conveniently generalized into other nonlinear problems. Thus, the findings and conclusions in this study will guide future research on the dynamic responses of general nonlinear mechanical systems.