Abstract
We study the deformation of an elastic strut on a nonlinear Winkler foundation subjected to an axial compressive load P . Using multi–scale analysis and numerical methods we describe the localized, cellular, post–buckled state of the system when P is removed from the critical load P = 2. The solutions, and their modulation frequencies, differ significantly from those predicted by weakly nonlinear analysis very close to P = 2. In particular, when P approaches the Maxwell load P M , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of P M in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.
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More From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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