Variational Feedback Control for a nonlinear beam under an earthquake excitation

The present paper reports on the application of the VFC (Variational Feedback Control) to the mitigation of the vibrational motion of continuous structures. The control method has been very recently proposed in the context of mechanical engineering to obtain suspensions characterized by better comfort performances. In this paper the same methodology is indeed applied to a simply nonlinear supported beam that is forced by a seismic excitation. The earthquake shaking, modelled as a random displacement of the beam hinges, is moderated by the presence of a controllable damper interposed between the beam and the oscillating ground, and its damping is subjected to the VFC controller. The inputs processed by the controller are the accelerations measured by two sensors, one on the ground, and the second on the beam. Numerical results are examined and some preliminary considerations are presented in which the considered method is applied to piezoelectromechanical beams.