Nonlinear vibrations of a rotor with support nonlinearities considering bounded uncertainties

Local nonlinearities induced by supports are common in rotor systems, such as cubic and non-smooth restoring forces. Moreover, inevitable uncertainties in such systems will interact with nonlinearities and the accurate tracking of nonlinear behaviors is challenging. This paper uses an arc-length ratio-assisted non-intrusive surrogate modeling method for uncertainty propagation in nonlinear vibrations of a rotor system with local nonlinearities. For the deterministic nonlinear solutions, the harmonic balance method coupled with the alternating frequency/time technique is used. The surrogate modeling in combination with arc-length ratio interpolations is formulated to enable efficient propagations of bounded parametric uncertainties in the nonlinear responses. Comprehensive case studies considering different uncertain parameters as well as numerical validations are carried out when the supports have different types of nonlinearities. It is shown that the non-intrusive surrogate function models are capable of predicting nonlinear vibrations of the nonlinear rotor system under bounded uncertainties with spurious peaks and the Gibbs phenomenon avoided. The findings of this study are useful for general nonlinear systems with complex behaviors since it is completely non-intrusive and requires no additional modifications to the original nonlinear solvers.

Automated summary

This paper investigates the propagation of uncertainties in nonlinear vibrations of a rotor system with local nonlinearities and proposes a non-intrusive surrogate modeling method. Through comprehensive case studies and numerical validations, it is shown that the proposed method can effectively predict the vibrational behavior of nonlinear rotor systems with bounded uncertainties.