DAMPED VIBRATION OF COMPOSITE PLATES WITH PASSIVE PIEZOELECTRIC-RESISTOR ELEMENTS

Mechanics for the analysis of damping in composite plates with multiple resistively shunted piezoelectric layers are developed. The mixed field piezoelectric laminate theory is extended to include distributed passive electric circuitry embedded or attached to piezoelectric layers. The equations of motion for the coupled laminate/circuitry system are formulated and exactly solved for the case of simply-supported plates. The modal frequencies and damping are directly calculated from the complex eigenvalues of the damped plate. The forced vibration of the damped piezoelectric composite plate is also directly predicted. Numerical results for a cross-ply graphite/epoxy plate with surface mounted resistively shunted piezoceramic layers are presented. The results show that for each mode there is an optimal resistance value which adds significant modal damping. Away from this optimal value the modal damping gradually reduces to zero. Simultaneous shifting of the corresponding modal frequency to a higher value occurs over this optimal resistance range. The calculated frequency response of the damped plate illustrates that substantial vibration control of select modes can be obtained by proper tuning of the shunting resistive circuit.