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The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems, however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of this method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

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