Dynamic response of planar cracks in an infinitely long piezoelectric strip

Abstract

The problem of determining the electro-elastic fields around an array of parallel planar cracks in an infinitely long piezoelectric strip is considered. The cracks, acted upon by dynamic loads, are either electrically impermeable or permeable. A semi-analytic method based on the theory of exponential Fourier transformation is presented for solving the problem in the Laplace transform domain. The Laplace transforms of the jumps in the displacements and electric potential across opposite crack faces are determined by solving a system of hypersingular integral equations. Once these displacement and electric potential jumps are obtained, the displacements and electric potential and other physical quantities of interest, such as the crack tip stress and electric displacement intensity factors, can be recovered with the help of a suitable algorithm for inverting Laplace transforms. The stress and electric displacement intensity factors are computed for some specific cases of the problem.