Exact solution for the vibration and active damping of composite plates with piezoelectric shear actuators

An exact three-dimensional solution is obtained for the cylindrical bending vibration of simply supported laminated composite plates with an embedded piezoelectric shear actuator. The piezoelectric actuator, which is poled in the longitudinal direction, will induce a transverse shear strain in the hybrid laminate when it is subjected to an electric field in the thickness direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equations that govern the steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations, which are solved by employing the power series method. Natural frequencies, mode shapes, displacements, electric potential and stresses are presented for three-layer hybrid laminates consisting of a piezoelectric shear actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using either a position feedback controller or velocity feedback controller. Frequency response curves for different controller frequencies, controller damping ratio and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is shown that vibration suppression of thickness modes is also feasible using a shear actuator.