Explicit finite-difference time-domain scheme for the simulation of 1-3 piezoelectric effect in axisymmetrical configurations

Numerical simulations are useful in the processes of design, development and optimization of transducers for non-destructive testing. In this work, a three-dimensional velocity–stress finite-difference model is presented for the elastic wave propagation in the piezoelectric substrate of a transducer excited by applying an impulsive voltage signal to the transducer electrodes. The allocation of the stress, velocity and electric field components on a staggered grid leads to a stable scheme. The different time scales of both mechanical and electromagnetic waves have leaded previous FDTD models to choose between significant physical simplifications or complicated implicit equations. The model presented here is explicit in all its time domain equations, contains only first order derivatives and is centered in time and space. The results of simulations show remarkable accuracy and stability for the different transducers studied.

► The centered finite difference time domain method for wavepropagation in piezoelectrics.
► A numerical model fully step-forward and centered in time and space.
► A model suitable for simultaneously variable electric and displacement fields.
► Stability condition due to mechanical wavespeed and infinite electromagnetic wavespeed.