The transient response of a piezoelectric strip with a vertical crack under electromechanical impact load

In this paper, the dynamic electromechanical response of a piezoelectric strip with a central crack vertical to the boundary was investigated. Based on the superposition principle and integral transform techniques, the present problem was reduced to the solution of two pairs of dual integral equations. To accommodate the ®nite size of the strip, two di€erent Fourier transforms, about the x and y coordinates, were assumed. The solution was obtained in the Laplace transformed domain in terms of Fredholm integral equations of the second kind by a modi®ed Copsonʹs method. The Laplace inversion was then carried out to obtain the resulting dynamic stress and electric displacement intensities. Unlike the ®ndings observed in the static fracture behavior of piezoelectric materials, the present study indicates that the dynamic electric ®eld will retard or promote the crack propagation at the di€erent loading stages. Furthermore, the dynamic electric response is proportional to the electric impact and is independent of the applied mechanical impact. It is also shown that both the mechanical and electric response around the crack tip are greatly in¯uenced by the free boundaries of the piezoelectric strip.