Liapunov Analysis of the Generalized Pfluger Problem

Abstract

A pin-ended column under an arbitrary tangential loading is considered. It is proved by the direct method of Liapunov that the mode of instability in all such problems is by divergence in the presence or absence of viscous damping, and an exact and simple criterion is given for the critical loadings. Two independent Liapunov functionals are also given for any such problem in the presence of arbitrary velocity-dependent loadings. These functionals are shown to provide exact stability results for a wide variety of such problems, and are believed to be the first ever found for the generalized Pflu¨ger problem.