Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation
E. Julius, Bassey
Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria.
M. Anthony, Ette
Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria.
U. Joy, Chukwuchekwa *
Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria.
C. Atulegwu, Osuji
Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increase in damping. The results obtained are strictly asymptotic and therefore valid as the parameters δ and ϵ become increasingly small relative to unity.
Keywords: Dynamic buckling, viscous damping, asymptotics and perturbation technique, column-like elastic structures.