Elastic stability of heavy rotating columns

Abstract

The stability of a cantilevered heavy column rotating with a constant angular velocity was investigated by Watson and Wang (1983). The governing differential equation for stability was derived from geometrical and static considerations. However, the differential equation is extremely difficult to solve, even upon linearization. This paper shows how this challenging problem can be easily solved via the Rayleigh-Ritz energy approach. As an extension to Watson and Wang's work, the column is also subjected to an axial load. An added advantage of using the Rayleigh-Ritz method is that a simple formula for predicting the buckling load can be readily obtained. Moreover, this technical note solves the buckling problem of continuously restrained columns and the free-vibration problem of columns, since the latter problems are shown to be similar to the stability problem of rotating columns.