Initial post dynamic buckling of a quadratic-cubic column pressurized by a sinusoidally slowly varying dynamic load

Abstract

In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains two small but Mathematically unrelated parameters upon which regular perturbation procedure are used in asymptotic expansions of the variables. The imperfection is assumed in the shape of the mth term in the Fourier sine series expansion with small (in absolute value) Fourier coefficients. A generalization of Lindsted-Poincare procedure is used and the structure under investigation is, on the main, a nonlinear oscillatory system with small perturbations. The results obtained are strictly asymptotic and are valid for small absolute values of the perturbation parameters. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 199-214