On an energylike functional for the calculation of buckling loads of completely supported rods subjected to follower forces (Q1075806)

Completely supported rods are the pinned-pinned, clamped-clamped and clamped-pinned rods. If these rods are subjected to uni-directional, uniformly distributed compressive forces, their respective lowest buckling loads can be calculated using the energy functional which leads to a respective Rayleigh quotient. This quotient has the actual buckling load of the corresponding rod as its lower bound. When the same rods are subjected to tangential, uniformly distributed compressive forces (compressive follower forces), they represent nonconservative systems. Therefore, the classical Rayleigh quotient can no longer be used. It has been shown by other means (Galerkin's method) that nonconservative rod systems are still of the divergence type, and that consequently their respective lowest critical loads are again buckling loads occurring at the frequency \(\pi\) \(\equiv 0.\) In this article it is shown that for systems of this type another functional, which is not the energy, but which is energylike, can be found which will serve as a tool for the derivation of a kind of generalized Rayleigh quotient. This new quotient yields an approximation to the buckling load.