Buckling of an elastic beam with added high-frequency excitation

A non-linear buckling analysis of an elastic beam subjected to an axial static force and high-frequency axial excitation is performed. A Galerkin beam discretization is applied and the method of direct partition of motion is used to obtain a set of autonomous model equations governing the slow averaged behavior. Adding high-frequency excitation increases the buckling load, but stable buckled equilibria may co-exist with the stabilized straight position. The influence of an imperfection in the system is discussed and so is the effect of modal truncation in the discretization.