Application of the Finite Element Method to the Design of Power Piezoelectric Sonar Transducers

Apart from the physical problem of the materials behaviour, the design of large bandwidth power piezoelectric transducers sets difficult problems which are associated with the bi-dimensional or tri-dimensional aspect of the structure geometries (ring or flextensional transducers, Helmholtz resonator…) or with the excitation of several vibrational modes. Then, the use of simple models, such as the equivalent circuits, is difficult, else impossible, and only the finite element method is able to provide an accurate modelling. This ṗaṗer describes the use of the finite element code ATILA to solve such problems. In the first part, the basic equations used for in-air modal analyses as well as in-water harmonic analyses are briefly described, including the presentation of an original mixed finite element-plane wave method. Then, the computations of eigenfrequencies and eigenmodes, displacement field, stress field, pressure nearfield and farfield are presented for different transducers (Tonpilz, ring and flextensional projectors) and numerical and experimental results are compared. Finally, several prospects are brought out : modelling of new materials and material losses, coupling with the integral equation method, optimisation.