On the repair of a cracked beam with a piezoelectric patch

In this paper, the repair of a cracked beam under an external load, employing the electro-mechanical characteristic of the piezoelectric material to induce a local moment, is presented. Conceptually, an external voltage is applied to actuate a piezoelectric patch bonded on the beam to effect closure of the crack so that the singularity induced by the crack tip may be eliminated. Using a simply supported beam as an illustration, the actuation voltage required is obtained from an equation containing variables such as the applied force, and the geometric and material properties of the beam and the piezoelectric material. It is shown mathematically and numerically that the voltage required (a) decreases linearly as the distance between the force and the location of the crack is increased, (b) varies quadratically with the position of the crack along the length of the beam, and (c) decreases hyperbolically as the ratio of the thickness of the piezoelectric patch to that of the beam increases.