Investigating the behavior of smart thin beams with piezoelectric actuators under dynamic loads
In this paper, the constitutive equation of motion for an Euler–Bernoulli beam in which a number of piezoelectric patches are bonded to the bottom and top surfaces of it, and arbitrary boundary conditions, is derived by employing Hamilton's principle. Assuming a number of linear springs with high stiffness as intermediate supports, the motion equation of a multi-span smart beam could be found. Classical linear optimal control algorithm with displacement–velocity and velocity–acceleration feedbacks is used. Utilizing eigenfunction expansion method, the equation of motion is decoupled into a number of ordinary differential equations. All the numerical examples are presented for the simple boundary conditions. The applied dynamic excitations are a rectangular impulse, moving load and the moving mass. Parametric studies on the capability of the control system in vibration suppression of the beams under these dynamic loads are achieved. The obtained results reveal the efficiency of the proposed control system in reducing the response of the beam structures to the required levels.