Asymptotic Analysis of the Static and Dynamic Buckling of a Column with Cubic - Quintic Nonlinearity Stressed by a Step Load

In this paper, the static and dynamic buckling loads of a viscously damped imperfect finite column lying on an elastic foundation with cubic – quintic nonlinearity but trapped by a step load (in the dynamic case) is investigated analytically. The main objective is to determine analytically both the static and dynamic buckling loads by means of perturbation and asymptotic procedures and relate both buckling loads in one single formula. The formulation contains small perturbations particularly in the viscous damping and imperfection amplitude. Multi – timing perturbation techniques and asymptotics are easily utilized in analyzing the problem. The results, which are nontrivially obtained, are implicit in nature and are valid as long as the magnitudes of the small perturbations become asymptotically small compared to unity.