Three-dimensional Vibration Suppression of an Euler-Bernoulli Beam via Boundary Control Method

In the present paper, general equations governing the beam vibration are derived in its three sub dimensions under the influence of system dynamics by using the Euler-Bernoulli beam theory and by utilizing Hamiltonian method. Then, two fundamental cases of a cantilever beam and a rotating beam are considered. Regarding the difficulty and the costliness of applying control commands to suppress the beam vibrations on its domain and regarding the difficulties of designing the controller based on the reduced and the discretized equations such as the control spillover and the boundary control method is both proposed and utilized. Thus, in order to suppress the beam vibration, control forces and moments placed on the system boundary are used. The controller which is designed based on the boundary control method and Lyapunov method guarantees the asymptotic stability of vibrations. The simulation results illustrate the high efficiency of the proposed method in suppressing the longitudinal and transversal vibrations of both states of cantilever and rotating beam with and without the boundary controller.