Vibration Suppression in Smart Thin Beams with Piezoelectric Actuators under a moving Load/Mass Accounting for Large Deflections of the Base Structure

In this article, the motion equations of a single span Euler-Bernoulli beam with geometrically nonlinear behavior under an arbitrary dynamic loading are derived via the Hamilton's Principle. In order to actively control the response of the structure, piezoceramic patches bonded on the lower surface of the beam are utilized. Employing the Eigen Function Expansion Method and considering the first vibrational mode, an equivalent linear control algorithm based on the well-known classical linear optimal control algorithm with displacement-velocity feedback is proposed. Numerical examples for a simply supported beam with immovable-immovable and immovable-movable axial boundary conditions are presented under a moving load and mass excitations. By using a single piezoceramic patch bonded symmetrically at the beam mid-span, the deflection of the beam is decreased into any required levels for both linear and nonlinear behavior of the base beam and therefore, the good performance of the proposed control algorithm is proved.