Vibration control of beams with active constrained layer damping

An analytical methodology is presented to study the active vibration control of beams treated with active constrained layer damping (ACLD). This analytical method is based on the conventional theory of structural dynamics. The process of deriving equations is precise and easy to understand. Hamilton's principle with the Rayleigh–Ritz method is used to derive the equation of motion of the beam/ACLD system. By applying an appropriate external control voltage to activate the piezoelectric constraining layer, a negative velocity feedback control strategy is employed to obtain the active damping and effective vibration control. From the numerical results it is seen that the damping performances of the beam can be significantly improved by the ACLD treatment. With the increase of the control gain, the active damping characteristics are also increased. By equally dividing one ACLD patch into two and properly distributing them on the beam, one can obtain better active vibration control results than for the beam with one ACLD patch. The analytical method presented in this paper can be effectively extended to other kinds of structures.