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

In this paper, the general governing equations of three-dimensional vibrations of an Euler-Bernoulli Beam under influences of system dynamics are derived by the Hamiltonian method. Then two fundamental cases of a cantilever beam and a rotating beam are considered. The conventional methods for vibration suppression debit to expenses and make new problems such as control spillover because they are based on reduced or discretized model. So, in order to suppress the beam vibrations the boundary control method is proposed to use. As the control command the boundary forces and moments on the beam ends are designed based on the Lyapunov method. These control commands guarantee the asymptotic stability of the system vibrations. The simulation results illustrate power of the proposed method to suppress the longitudinal and transverse vibrations of the cantilever and the rotating beams.