Active control of bending vibrations of Timoshenko beams using state observers

When describing bending vibrations of elastic beams, the transition from the Bernoulli — Euler model to the Timoshenko model leads to a complication in the dynamic behavior of the beam and to the emergence of new dynamic effects and a new spectrum of vibration modes. The aim of this study is to test control approaches developed for Bernoulli — Euler beams, for thicker beams described by the Timoshenko model, and to study the influence of beam thickness on the efficiency of such approaches. For this purpose, the problem of active damping of forced bending vibrations of simply supported metal beams has been studied numerically using control systems with state observers, where point forces or moments serve as control inputs. It was shown that the proposed approach remained effective for the vibration control problem of Timoshenko beams at lower modes over a wide thickness range of the considered beams.