Modeling of axisymetrical transducer configurations based on pseudospectral/finite-difference time-domain method

The transient analysis of piezoelectric resonators with complex shape is often performed using finite-element (FE) methods whose numerical dispersion prevents the modeling of waves propagating over large distances. Although this difficulty can be countered by the successive use of several models (one to model structure vibrations, an other to simulate acoustic propagation), the purpose of this work is to develop a single numerical algorithm which enables to accurately simulate both the generation of acoustic waves in a piezoelectric transducer and their propagation In the surrounding media. The pseudospectral time-domain (PSTD) algorithm is used to simulate the propagation of acoustic waves, as stability and high accuracy can be achieved from as few as two nodes per wavelength. But the electric field can not be calculated with this method. That Is why piezoelectricity is implemented using a finite-difference (FD) representation, resulting in an hybrid FD-PSTD model which retains the advantages of both methods. The axisymmetrical computation of the algorithm is exposed and the results obtained for the simulation of HE transducers are found to be in agreement with those of the FE algorithm of ATILA (R) software.