Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 1

On the chaotic behavior of a compressed beam

Pages: 55 – 86

DOI: http://dx.doi.org/10.4310/DPDE.2007.v4.n1.a2

Authors

Flaviano Battelli (Dipartimento di Scienze Matematiche, Università di Ancona, Italy)

Michal Feckan (Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Bratislava, Slovakia)

Matteo Franca (Dipartimento di Scienze Matematiche, Università di Ancona, Italy)

Abstract

We study a PDE modelling a compressed beam with small friction and subjected to a periodic forcing of small amplitude. We assume that the load of the beam is resonant to the i-th eigenvalue of the associated unperturbed problem and prove that, when both forcing and damping are sufficiently small the equation exhibits chaotic behaviour.

Keywords

compressed beam, chaotic solutions, bifurcation

2010 Mathematics Subject Classification

35-xx, 37-xx

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