Lumped damping and stability of Beck column with a tip mass

Abstract

Lumped external damping, acting on the concentrated mass at the tip of Beck’s column, is taken into account. This additional external damping removes the prolonged inconsistency between theory and experiment for a column with a tip mass, subjected to follower force. In Sugiyama et al. [J. Aerospace Eng. 8 (1995) 9] and Wood et al. [Proc. Roy. Soc. Lond. Ser. A. 313 (1969) 239] the experimental critical loads for a beam with a tip mass agree well with theoretical values for an undamped system. On the other hand, the critical loads, calculated in Sugiyama et al. with account for the internal and distributed external damping, were 50% lower than the experimental values. Since the actual experimental system is subject to damping, the experiment and theory come into conflict. This conflict is resolved in this paper by observing that the experimental system was subjected not only to the distributed external damping (due to distributed mass), but also to the lumped damping, acting on the tip mass. When the lumped external damping included in the analysis, analytical critical forces are in good agreement with experimental ones.