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Solitary wave interaction phenomena in a strut buckling model incorporating restabilisation

journal contribution
posted on 2023-05-18, 17:51 authored by Wadee, MK, Coman, CD, Andrew BassomAndrew Bassom
The archetypal model of the buckling of a compressed long elastic strut resting on a nonlinear elastic foundation is studied. Localised buckling is investigated when the foundation has both quadratic and cubic terms which initially destabilise but subsequently restabilise the structure. The primary solution can be detected by a double-scale perturbation procedure and is reminiscent of a solitary wave: essentially, it consists of a fast periodic oscillation which is slowly modulated and decays exponentially in both directions. Particular interest is paid to the process of adapting the procedure to account for the post-buckling behaviour of two-packet or double-humped solitary waves in this model. We employ the methods of beyond-all-orders asymptotics to reveal terms formally exponentially small in the perturbation parameter which have macroscopic effects on the post-buckling behaviour of the system including the interaction phenomenon of interest. The analysis is reinforced by direct numerical computations which reveal the so-called snaking behaviour in the subsidiary homoclinic orbits as is observed in the case of primary solutions. However, additional phenomena arise for these subsidiary forms including the formation of bridges linking solution paths and the appearance of a multitude of closed isolated loops disconnected from other features of the bifurcation diagram.

History

Publication title

Physica D - Nonlinear Phenomena

Volume

163

Issue

1-2

Pagination

26-48

ISSN

0167-2789

Department/School

School of Natural Sciences

Publisher

Elsevier Science Bv

Place of publication

Po Box 211, Amsterdam, Netherlands, 1000 Ae

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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