A direct numerical method for the determination of instability threshold and stability boundaries of flexible rotor-bearing systems is presented. The proposed procedure can also be used to improve the system stability by considering the design variables as operating parameters. The finite element method is utilized in the formulation of system equations of motion. The numerical algorithm is based on nonlinear optimization techniques. Two examples are presented to illustrate the feasibility, desirability, and ability of the proposed algorithm. A simple journal bearing system is used for the parametric study. An industrial high-speed compressor is employed to demonstrate the ability of this algorithm to deal with practical applications. The stability boundaries calculated from this algorithm are in agreement with the experimental results.

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