Phase driven study for stochastic linear multi-dofs dynamic response

Abstract

This work addresses the computation of dynamic responses of stochastic linear systems using polynomial chaos expansion. As is now well known, polynomial chaos does not offer an accurate representation of dynamic response around resonances when the responses are evaluated for several frequency values. A new parametrization of the frequency response function is then proposed: instead of considering the frequency as the main parameter, a "total phase" parameter is defined and used to define the dynamical system to be solved. It is shown via two applications that this approach offers very accurate results when conjugated to polynomial chaos with low degree.

A state-of-the-art review on uncertainty analysis of rotor systems

“…An intrusive PCE was implemented in the HBM process to build the nonlinear response from a limited number of runs of the computational model. Sarrouy et al [230,231] proposed to use the phase of vibration as a new control parameter in linear stochastic systems to eliminate multimodality and discontinuity in FRFs. This viewpoint may also be inspiring for solving the multi-solution issue in nonlinear systems with uncertainties although till now no relevant research has been reported to clarify how to transfer back to the frequency measure from the phase measure.…”