The study deals with the instability and unbalance response of dissymmetric rotors, when periodic differential equations are impossible to avoid. The method which yields motion instability is based on an extension of the well-known Floquet theory. A transfer matrix over one period of the motion is obtained, and the stability of the system can be tested with the eigenvalues of the matrix. To find the instability and the unbalance response, the Newmark formulation is used. Here, the dissymmetry comes either from the rotor or from the bearings in such a way that it is possible to solve a regular differential system without periodic coefficients, either in the stationary coordinate system or in the rotating one. Three examples are given, including an industrial application. The results show that the method proposed is satisfactory.

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