Modal analysis of cracked beam with a piezoelectric layer

Piezoelectric material was employed first as sensor/actuator for structural control and then it has got an effective use for structural health monitoring and repairing damaged structures. In this report, modal analysis of cracked beam with piezoelectric layer is carried out to investigate effect of crack and piezoelectric layer thickness on natural frequencies of the structure and output charge generated in the piezoelectric layer by vibration modes. Governing equations of the coupled structure are established using the double beam model and two-spring (translational and rotational) representation of crack and solved to obtain the modal parameters including the output charge associated with natural modes acknowledged as modal piezoelectric charge (MPC). Numerical examples have been examined for validation and illustration of the developed theory.