Comparison of dynamic response of a piezoelectric ceramic containing two parallel cracks via two methods of Laplace inversion

The dynamic interaction of two parallel insulting cracks in a piezoelectric material is studied under the action of antiplane mechanical and inplane electric impacts. Using two different methods for performing a numerical inversion of the Laplace transform, dynamic field intensity factors are obtained numerically. By comparison, results indicate that use of Fourier series approximation is more efficient than use of Jacobi polynomials in performing the inverse Laplace transform. Based on the former approach, some typical transient features including the time of the occurrence of an overshoot, and the arrival of wave-front, etc. manifest at the response curves, which reveals clearly the effects of the distance between two cracks on dynamic stress intensity factors.