On the dynamic buckling of a lightly damped elastic cubic model structure modulated by sinusoidally slowly varying load

Abstract

In this paper, we employ a generalization of Lindsted-Poincare technique to determine the dynamic buckling load of a lightly and viscously damped elastic cubic model structure modulated by a sinusoidally slowly varying dynamic load. The imperfect elastic cubic (nonlinear) structure is itself a generalization of most elastic physical structures that have been investigated over the years. The formulation contains two small but mathematically unrelated parameters upon which asymptotic expansions are initiated. The dynamic buckling load is obtained asymptotically and is related to the result corresponding to that of the static loading. This process by-passes the labour of repeating the entire process for different imperfection parameters.

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 187-198