Asymptotic analysis of the dynamic stability of a viscously damped elastic model structure under step load

Abstract

In this paper we determine the dynamic stability of a viscously damped elastic model structure subjected to step load (load suddenly applied and held constant). Here, consideration is extended to buckling under loading history characterized by an infinite length of time of load application. Asymptotic expansions and perturbation method are used to solve the non-linear second order differential equation that emanated from the dynamic equilibrium. The elastic model structure is itself a generalization of most real structures. The result shows that damping diminishes the vibration amplitude thereby increasing the dynamic bucking load and also, that increase in geometric imperfections decreases the dynamic buckling load.