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 / Battelli, Flaviano; M., Feckan; Franca, Matteo. - In: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1548-159X. - STAMPA. - 4:1(2007), pp. 55-86.