### 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 PM , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of PM in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.

Original language | English |
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Pages (from-to) | 2935-2964 |

Number of pages | 30 |

Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |

Volume | 457 |

Issue number | 2016 |

DOIs | |

Publication status | Published - 2001 |