Nonlinear responses of a dual-rotor system with rub-impact fault subject to interval uncertain parameters

This paper aims to study the nonlinear steady-state response of a dual-rotor system with rub-impact fault subject to unknown-but-bounded (UBB) uncertainties. Mathematical modelling of the non-linear dynamical system is carried out based on the Lagrangian formulation. The nonlinear dynamic response of the rubbing dual-rotor system without uncertainty is solved by using the multi-dimensional harmonic balance method coupled with the alternating frequency/time technique. The arc-length continuation is used to track the solution branches. To predict the response range subject to uncertainty, a non-intrusive surrogate model in conjunction with the polar angle interpolation (PAI) with efficiency enhancement is developed to track the propagations of parametric variabilities. The PAI is dedicated to dealing with collocations where the responses have multiple solutions. Effects of UBB variables in the physical model and fault-related parameters are investigated comprehensively. Different features of the variabilities in the steady-state responses are found under the typical uncertain degrees. The interval scanning method is used to validate the computation accuracy of the whole procedure. Moreover, the working mechanism of the PAI method is demonstrated via examples in detail. The results obtained in simulations can provide useful guidance for the nonlinear dynamic investigations and rub-impact fault diagnosis of dual-rotor systems under the UBB uncertainties. The proposed non-intrusive uncertainty quantification framework based on the PAI will also be beneficial to other nonlinear vibration problems where multiple solutions are involved.