Sensitivity analysis of the rotor-bearing system with fractional power nonlinearity using multicomplex variable derivation

In the computation of dynamic response sensitivity for rotor-bearing systems using the multicomplex variable derivation method, the presence of nonlinearity, particularly “fractional power” nonlinearity, in the forces generated at the supports may introduce rounding errors, potentially destabilizing the sensitivity calculation results. To address this issue, this paper proposes an enhanced method for sensitivity calculation using multicomplex variable derivation method. The approach leverages De Moivre’s theorem to conduct recursive operations on multicomplex numbers, thereby circumventing the rounding errors associated with the “fractional power” nonlinearity. This method facilitates the simultaneous calculation of sensitivity for each order and hybrid sensitivity. Subsequently, the viability of the proposed method is substantiated through a nonlinear single disk rotor system and a simulated gas generator rotor system. The results demonstrate that the proposed method maintains high accuracy and stability in dynamic response sensitivity computations even in the presence of “fractional power” nonlinearity.