A simple method to evaluate the critical loads of cantilever columns with follower forces

Abstract

A simple method, based on two term Galerkin method, is presented here to evaluate the critical loads of a uniform cantilever column with follower forces. Three types of follower forces are considered. If two terms are used in the Galerkin method, a quadratic equation for the frequency is obtained and the critical loads are evaluated by making the radical of the solution of the quadratic equation zero, avoiding a frequency mapping with the applied follower force. When the radical is zero, the value of the frequency obtained is the coalescence frequency. The accuracy of results obtained from the present method is quite suitable for engineering purposes. The accuracy can further be improved if suitable admissible functions, which represent the first two modes of vibration accurately, are chosen.