On the Vibration of a Rotating Shaft System Having Two Rotors

In this paper, the vibration and the critical speed of a rotating shaft having two rotors are treated theoretically considering the gyroscopic effect of the rotors and the distributed mass of the shaft. A symmetrical shaft system in which both rotors are symmetrical and an asymmetrical one in which rotors and the bending rigidity of the shaft are asymmetrical are treated using different coordinate systems respectively, and the eigen-frequencies at any shaft speed and the critical speeds are calculated exactly. An approximate formula for the lowest critical speed of a symmetrical rotating shaft system having n rotors by Rayleigh's method and one for critical speeds of higher order by Ritz's method are obtained considering the gyroscopic effect of the rotors, and numerical examples are shown.