The various self-excited oscillation regimes of flexible gyroscopic rotors are considered. The movement of the analyzed structures is described by quasi-linear non-uniform differential equations in partial derivatives. Vibrations in the instability fields of their bending vibrations have a quasi-periodic self-excited character. The method of direct division of displacements and a procedure for constructing equations of motion for quasi-periodic solutions are proposed. Two self-excited oscillation regimes are possible: non-resonant and resonant (critical). Most attention is paid to the resonant case, for which stationary equations satisfying the sought self-excited vibrations are derived.
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