This paper treats unstable vibrations of a rotating asymmetric shaft supported by upper and lower flexible bearing pedestals each of which has a directional inequality in stiffness and a concentrated mass. The position, width and number of the instability regions and a dynamic behavior of the shaft are analytically obtained by approximation. As a result, it is determined simply by one parameter that each unstable region which is caused only by asymmetry of the rotating shaft is split up into several parts (one, two, three, or four regions) by the directional stiffness inequality of bearing pedestals. Instability regions derived from approximation were found to agree well with those obtained by analog computer.

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