The Effect of external Damping on the Stability of Beck's Column

Abstract The stability of a cantilevered column subjected to a constant follower load in the presence of external damping is investigated. It is shown that the critical load increases with increasing damping from the value of 20.05 EI/L 2 at zero damping to the limiting value of 37.7 EI/L 2 for large damping. This behavior is in marked contrast to that of the internally damped column and also to that of conservative systems (where external damping has no effect on the critical load). The results of this analysis, which are based on a modal approximation, are corroborated by the results obtained from the study of a standard two-degree-of-freedom model of the continuous column. Further confirmation is obtained from a computer analysis of the exact frequency equation.