Three-dimensional Lamb wave propagation excited by a phased piezoelectric array

A dielectric-mechanical coupled finite element formulation from partial differential equations is derived, and the formulation is implemented in the framework of FEAP (Taylor 2008 FEAP-A Finite Element Analysis Program, Version 8.2 User Manual University of California at Berkeley). For the enhancement of the calculation efficiency in the three-dimensional simulation, a partitioned solution scheme is utilized, and time integration is implemented explicitly for the mechanical part. A comparison of the numerical results in two-and three-dimensional Lamb wave propagations is performed, and the formation of the Lamb waves and the tangential stress distribution imposed on the aluminum plate by a lead-zirconate-titanate (PZT) patch are investigated. A virtual Lamb wave phased array comprised of 16 PZT patches is developed by tuning the symmetric mode of the Lamb wave to be dominant. The 16 PZT patches are excited individually, aiming at a point, and the numerical result shows good agreement as regards the estimated times of arrival and the focused response at the target point.