On the Forced Vibrations of the Shaft Carrying an Unsymmetrical Rotor : Forced Vibrations Having the Circular Frequencies Differing from the Rotating Angular Velocity of the Shaft

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When the unsymmetrical rotor with angular velocity ω is excited by a periodic external force having frequency ω₀, two forced vibrations of frequencies ω₀ and ω₀'=2ω-ω₀ take place simultaneously. Depending on the circumstances, the amplitudes of the vibration of frequency ω₀'become remarkably larger than the amplitudes of the harmonic oscillation, i.e., the forced vibration of frequency ω₀. Thus the idea generally accepted for the forced vibrations, that"the frequency of the forced vibration is equal or relates to that of the external force"is not always applicable for the forced vibrations of the shaft carrying an unsymmetrical rotor. In the present paper the response curves, the amplitude ratio between two forced vibrations, the effects of the damping forces are discussed analytically, and the obtained results are ascertained through the experiments.