On the dynamic Stability of a quadratic-cubic elastic model structure pressurized by a slowly varying load

Abstract

The main substance of this investigation is the determination of the dynamic buckling load of an imperfect quadratic-cubic elastic model structure , which ,in itself, is a Mathematical generalization of some of the many physical structures normally encountered in engineering practice and allied fields. The load function in which the time variable is explicitly expressed, varies very slowly over a natural period of oscillation of the structure. The nonlinearity is quadratic-cubic in nature and multiple-scaling two-timing regular perturbation technique is utilized. The result shows that the dynamic buckling load depends on the first derivative of the load function evaluated at the initial time .Besides , it is established that it is possible to relate the dynamic buckling load to its static equivalent and this by-passes the labour of repeating the entire arduous process for different imperfection parameters .

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 185-196