Effects of piezoactuator delamination on the transfer functions of vibration control systems

The purpose of this theoretical work is to present a general bending±extensional model of the response of a simply supported laminated beam to excitation by a nonsymmetric actuator made using piezoelectric elements. The edge delamination is modeled by changing the e€ective length of debonded actuator. Dynamic equations, joint conditions between sections with and without active layers as well as the boundary conditions at the two ends of the beam form a boundary value problem. The dynamic strain response to the excitation by the applied voltage term is determined from the solution of this boundary value problem. The dynamic extensional strain on the beam surface is calculated by including the free stress conditions at the piezoelectric actuator boundaries, by considering the dynamic coupling between the actuator and the beam, and by taking into account a ®nite bonding layer with the ®nite sti€ness. The analysis indicates that the edge delamination has a harmful e€ect on the performance of piezoactuators, but the signi®cant decrease of natural frequencies with an increase in delamination length is not observed. The in¯uence of the delamination length on the system transfer functions (the beam surface strain, the beam transverse displacement and the shear stresses in bonding layers) is shown