Stability of an Elastic Column Subjected to Non-Stationary Compressive Loads

The problem of dynamic stability of an elastic column with pinned ends subjected to non-stationary compressive axial loads is considered. The method of optimal Lyapunov functions for differential inclusions is applied to obtain sufficient conditions of stability of the column in the case of bounded loads. The obtained results, improving and generalising the classical solutions to the dynamic Euler problem, may be useful in designing civil engineering structures and mechanical systems consisting of compressed columns. The possibility of optimisation of the column characteristics with respect to its stability properties (e.g. stability margins in the space of parameters) is pointed out.