The scattering of flexural waves of a symmetric piezoelectric laminated plate with a through crack

Following the theory of linear piezoelectricity, we consider the dynamic bending of a cracked composite plate with attached piezoelectric polyvinylidene fluoride layers subjected to electric field loading and incident flexural waves. The input waves are generated by a combination of bending moments applied to the plate edge causing the plate to vibrate in the transverse direction, and the electric field and the poling direction are perpendicular to the plate surfaces. Fourier transforms are used to reduce the mixed boundary value problem to the solution of a pair of dual integral equations. The integral equations are further reduced to a Fredholm integral equation of the second kind. Numerical results are given for the dynamic moment intensity factor versus frequency for several values of the electric field and the geometrical parameters.