DYNAMIC STABILITY OF INITIALLY CROOKED COLUMNS UNDER A TIME-DEPENDENT AXIAL DISPLACEMENT OF THEIR SUPPORT

Abstract

A simple and very efficient technique for the solution of the initial-value problem of dynamic stability of an initially crooked, simply supported column subjected to a time-dependent axial support displacement is presented. Convergence, uniqueness and error estimates of the solutions obtained by the iteration scheme of the proposed method are also established. From the error upper bound of these solutions important conclusions regarding the improvement of convergence required for long periods of time solutions are given. The advantage of this approximate method to obtain results of any accuracy using simple formulae is shown with the aid of existing results which are also checked by means of the Runge-Kutta scheme.