On the dynamic buckling of a weakly damped nonlinear elastic model system under a slowly varying explicitly time dependent load

Abstract

In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular perturbation method is used in asymptotic expansions of the variables. The elastic model structure is itself a generalization of most physical elastic structures in common use in Structural Engineering .The dynamic buckling load is obtained nontrivially and compared with related previous results of similar loading conditions. The result shows that the dynamic buckling load does not depend on any particular form of the loading function but depends on the first and second derivatives of the loading function evaluated at the initial

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 165-174