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.
On the chaotic behavior of a compressed beam / F. BATTELLI, M. FECKAN, M. FRANCA. - In: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1548-159X. - STAMPA. - 4:(2007), pp. 55-86.
On the chaotic behavior of a compressed beam
M. FRANCA
2007
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.
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