The Lateral Vibrations of an Axially Rotating Bar

Introduction: It has long been known that the rotational motion of a bar or shaft at certain speeds is capbable of exciting lateral vibrations of the shaft. Almost invariably these vibrations are undesirable or even destructive, and for this reason considerable attention has been given to their study. The subject has a fairly extensive literature dating back to 1869 when Rankine^1,2 first treated the stability of a shaft, running true and in perfect balance, against small disturbances. His results were erroneous because he assumed that the plane of vibration always rotated with the shaft, which is equivalent to neglecting the Coriolis force. Amazingly, this assumption has proved irresistible to many authors since his time, dating well into the present century.