Two-dimensional transient analysis of wave propagation in functionally graded piezoelectric slabs using the transform method

In this study, the transient responses of a functionally graded piezoelectric slab were analyzed using the transform technique. The slab was subjected to a dynamic anti-plane concentrated force and an in-plane point electric displacement on the top surface, and the bottom surface was assumed to be open-circuit or grounded. The analytical solutions were obtained in the Laplace transform domain, and a numerical inversion was performed using the Durbin method. The numerical results showed that an applied point electric displacement may instantaneously induce shear stress waves due to the piezoelectricity for both open-circuit and grounded cases. When the bottom surface was grounded, a visible electric wave was induced by the grounded boundary and the influence of this wave was significant when the gradient coefficient of the functionally graded piezoelectric materials (FGPMs) was large enough.