Dynamic stability of a lightly damped column trapped by a harmonically slowly varying explicitly time dependent load

Abstract

In this paper we initiate an analytical approach for determining the dynamic buckling load of a finite viscously damped column acted upon by a harmonically slowly varying explicitly time dependent load. The viscous damping is considered light and the column rests on an elastic foundation that produces a nonlinear restoring force per unit length. Unlike most similar analyses, the time variable appears explicitly making the problem non-autonomous the formulation contains two small but unrelated parameters upon which asymptotic expansions are initiated. The coefficients are sinusoidally slowly varying and problem is solved using a generalization of Lindsted-Poincare method in a mulit-timing regular perturbation technique. Simple asymptotic results implicit in the load parameter are obtained. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 149-156