The analysis and design of rotor-bearing systems with gyroscopic effects are discussed in this paper. The original problem of this nonproportionally damped mechanism is transformed into the state space form so that the transformed problem is similar to the eigenvalue problem for an undamped system. It can be easily solved by widely available eigensolvers and the eigenvalue sensitivities needed for the design optimization can also be obtained conveniently using the transformed form. The sequential linear programming technique is employed to solve the design optimization problem. The easy implementation of this proposed approach with a general purpose finite element program is shown in the solution algorithm.

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