Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load

Main Article Content

A. M. Ette
I. U. Udo-Akpan
J. U. Chukwuchekwa
A. C. Osuji
M. F. Noah

Abstract

This investigation is concerned with analytically determining the dynamic buckling load of an imperfect cubic-quintic nonlinear elastic model structure struck by an explicitly time-dependent but slowly varying load that is continuously decreasing in magnitude. A multi-timing regular perturbation technique in asymptotic procedures is utilized to analyze the problem. The result shows that the dynamic buckling load depends, among other things, on the first derivative of the load function evaluated at the initial time. In the long run, the dynamic buckling load is related to its static equivalent, and that relationship is independent of the imperfection parameter. Thus, once any of the two buckling loads is known, then the other can easily be evaluated using this relationship.

Keywords:
Dynamic buckling, perturbation approach, multi-timing perturbation technique, cubic-quintic nonlinear elastic structure, slowly varying load, imperfection parameter.

Article Details

How to Cite
Ette, A., Udo-Akpan, I., Chukwuchekwa, J., Osuji, A., & Noah, M. (2019). Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load. Journal of Advances in Mathematics and Computer Science, 32(6), 1-19. https://doi.org/10.9734/jamcs/2019/v32i630160
Section
Original Research Article

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