Bending-vibration control of composite and isotropic plates through intelligent constrained-layer treatments

In this paper intelligent constrained-layer (ICL) damping treatments are applied to control bending vibration of composite and isotropic plates. The ICL damping treatment consists of a viscoelastic shear layer sandwiched between a piezoelectric constraining cover sheet and the structure to be damped. According to the measured vibration response of the structure, the feedback controller regulates axial deformation of the piezoelectric layer to perform active vibration control. The equation of motion and boundary conditions governing the bending vibration of a composite plate processing bending-stretching coupling stiffness with ICL damping treatments are derived. Two examples are illustrated in this paper. The first example considers an infinite composite plate consisting of a &plusmn45° angle ply laminate subjected to plane harmonic wave excitations. An ICL treatment with an idealized, distributed sensor and a proportional-plus-derivative feedback controller is used to control the bending vibration of the composite plate. Compared with existing passive constrained layer treatments, numerical results show that the ICL damping treatment can produce significant damping. In addition, there are certain orientations, determined by the structures of the composite laminate, along with the vibration amplitude can be reduced to a minimum. The second example considers bending-vibration control of a simply supported rectangular, isotropic classical plate through use of ICL treatment. The equation of motion is first obtained from that of the composite plate with the bending stiffness matrix, the extensional stiffness matrix, and the bending-extension coupling stiffness matrix replaced by isotropic elastic constants. A four-mode Galerkin approximation shows that the vibration amplitude of the first bending-vibration mode can be reduced significantly through ICL. The second bending-vibration mode, though uncontrollable for a simply-supported rectangular plate, will have finite amplitude because of the passive damping of the ICL.