Active Non-Linear Control of a Buckled Beam

Buckled beams have been used in several engineering applications to support lateral loading. These arch-like structures are highly nonlinear and may display several instability phenomena when subjected to dynamic and static loads. In this paper a certain class of optimal non-linear control algorithms is used to control the oscillations of simply supported buckled beams subjected to transversal distributed load. To control the non-linear oscillations of the arch, concentrated moments are applied at suitable points along the beam axis. The results show that the proposed control scheme can not only mitigate the effects of dynamic loading on the vibration amplitudes of the beam but also prevent dangerous instability phenomena. In fact the numerical results indicate that the control algorithm can effectively increase the load-carrying capacity of the beam without demanding large control forces.