Asymptotic solution on the dynamic buckling of a column stressed by a dynamically slowly varying load

Abstract

This paper analysis the dynamic stability of a dynamically oscillatory system with slowly varying time dependent parameters. It utilizes the concept of multiple times scaling in an asymptotic evaluation of the dynamic buckling load of the imperfect elastic structure under investigation. Unlike most similar investigations to date , the time dependence is explicit in the formulation and this creates a situation of non-autonomous differential equation that accurately models the dynamic stability of the structure .The dynamic buckling load is obtained nontrivially and the results are found to generalize earlier results obtained for step loading situation. It is established that the results depend strongly on the first derivative of the load function evaluated at the initial time.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 197-202