 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A. M. Ette, G. E. Ozoigbo, J. U. Chukwuchekwa, W. I. Osuji, and A. C. Osuji, "On the Dynamic Buckling of a Pre – Statically Loaded Cubic Elastic Model Structure Struck by a Slowly Varing Explicitly Time Dependent Load," Mech. Solids. 57 (2), 412-426 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
2 |
Pages |
412-426 |
| DOI |
10.3103/S0025654422020157 |
| Title |
On the Dynamic Buckling of a Pre – Statically Loaded Cubic Elastic Model Structure Struck by a Slowly Varing Explicitly Time Dependent Load |
| Author(s) |
A. M. Ette (Department of mathematics, Federal University of Technology, Ow - Erri. Imo State, Nigeria, tonimonsette@yahoo.com)
G. E. Ozoigbo (Department of mathematics, Federal University of Technology, Ow - Erri. Imo State, Nigeria; Department of Mathematics/Computer Science/Statistics & Informatics, Alex Ekwueme Federal University Ndufu - Alike, Ikwo. Ebonyi State, Nigeria, geraldozoigbo@yahoo.co.uk)
J. U. Chukwuchekwa (Department of mathematics, Federal University of Technology, Ow - Erri. Imo State, Nigeria, joyuchukwukwa@yahoo.com)
W. I. Osuji (Department of mathematics, Federal University of Technology, Ow - Erri. Imo State, Nigeria, osujiwillians03@yahoo.com)
A. C. Osuji (Department of mathematics, Federal University of Technology, Ow - Erri. Imo State, Nigeria, chukusosuji@yahoo.com) |
| Abstract |
The dynamic buckling of a statically pre-loaded cubic elastic model structure that is later struck by a dynamically slowly varying load is here analysed by means of perturbation procedures using asymptotic expansions. The nonlinear formulation contains some nondimensional but small parameters that enhance the asymptotic expansions in a multi-timing regular perturbation analysis. Apart from being dynamically slowly varying, the loading history is also explicitly time dependent and infinitely differentiable with right hand derivatives of all orders at the initial time. To the order of the accuracy retained, the result shows that the dynamic buckling load depends on the first derivative of the loading history evaluated at the initial time. It is similarly observed that the pre–static load has effect only on the nonlinear component of the equation of motion. We are able to relate the dynamic buckling load to the equivalent static buckling load, hence, one of these two loads can be readily obtained if the other one is already known. Specializations are made to the case of a step load that is with or without a pre-static load. Such results are seen to be in agreement with previous results. |
| Keywords |
Slowly varying, infinitely differentiable, perturbation, pre-statically loaded, cubic elastic model |
| Received |
14 April 2021 | Revised |
09 July 2021 | Accepted |
09 July 2021 |
| Link to Fulltext |
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