Numerical Assessment of Using Sherman-Morrison, Neumann Expansion Techniques for Stochastic Analysis of Mistuned Bladed Disc System

The paper presents an assessment about using two classical reduced-order techniques, the Sherman-Morrison-Woodbury (SMW) formula and the Neumann expansion method, to enhance the computational efficiency of the stochastic analysis in mistuned bladed disc systems. The frequency responses of the blades are evaluated for different mistuning patterns via stiffness perturbations. A standard matrix factorization method is used as baseline to benchmark the results obtained from the SMW formula and Neumann expansion methods. The modified SMW algorithm can effectively update the inversion of an uncertainty matrix without the need of separated inversions, however with a limited increase of the computational efficiency. Neumann expansion techniques are shown to significantly decrease the required CPU time, while maintaining a low relative error. The convergence of the Neumann expansion however is not guaranteed when the excitation frequency approaches resonance when the mistuned system has either a low damping or high mistuning level. A scalar-modified Neumann expansion is therefore introduced to improve convergence in the neighbourhood of the resonance frequency.