Stability of general asymmetric-anisotropic rotors subject to harmonic follower force

Abstract

The presented work examines the stability of general rotors subject to harmonic follower force. The examined rotor consists of asymmetric Timoshenko shaft carrying asymmetric rigid disk and supported by anisotropic flexible bearings. The assumed modes method is combined with Lagrange’s equation to derive the governing equations of motion with the help of symbolic computation. The employed approach resulted in equations of motion with multi-frequency periodic coefficients, and Floquet’s method was used to determine stability boundaries of the considered rotors. After validation of the proposed mathematical model, it was employed to examine the combined effect of rotor asymmetry, support anisotropy, and rotor speed on its stability in the presence of harmonic follower force. The presented results show that the considered general rotor exhibits both subharmonic and combination instabilities, which were completely identified and investigated. Additional higher order subharmonic and combination instabilities are observed for general rotors only.