Nonlinear Dynamic Buckling Behaviour of Viscously Damped Columns on Elastic Foundations Under Step Loading

Abstract

This study investigates the influence of viscous damping on the load-carrying capacity of an imperfect finite column. The analysis is based on an established governing equation for the lateral displacement of a viscously damped finite column, which is solved using the regular perturbation method. To facilitate the solution, the governing equation is first non-dimensionalized through the introduction of appropriate dimensionless parameters. This transformation naturally introduces a slow time scale into the formulation, and nonlinear terms of order higher than cubic are neglected to simplify the analysis. The resulting expression for the lateral displacement, as a function of both time and spatial coordinates, is derived analytically. An asymptotic series expansion is then employed to determine the column’s maximum lateral displacement, from which the dynamic buckling load is obtained. The actual buckling load values are computed using MATLAB, and the results are subsequently used to assess the quantitative effect of viscous damping on the dynamic buckling capacity.