Eigensolution Variability of Asymmetric Damped Systems

The characterization of energy dissipation or damping in rotor dynamic model is of fundamental importance. Noise and vibration are not only uncomfortable to the users, but also may lead to fatigue, fracture and even failure. During the design process of asymmetric damped systems, it is often required to make changes in the design variables such that the design is optimal. This paper is aimed at developing computationally efficient numerical methods for parametric sensitivity analysis. The algebraic method considered here computes the eigenvector sensitivity by assembling the derivatives of eigenproblems and the additional constraints into an algebraic equation. The coefficient matrix may be ill-conditioned since the elements of it are not all of the same order of magnitude. In this study, a new algebraic method is presented to compute the eigensolution variability of asymmetric damped systems. Some weight constants are introduced such that the proposed method is well-conditioned. The method is very compact and highly efficient, and the numerical stability is also demonstrated. Moreover, several special cases can be presented based on the similar idea of the proposed method. Finally, two numerical examples show the validity of the proposed method.