Finite element modeling of acoustic transducers

In recent years, the need for designing piezoelectric or magnetostrictive acoustic transducers with actually three-dimensional geometries and thus exhibiting complex displacement fields has become urgent. This is the case in underwater acoustics, for sonar or oceanographical applications, with the renewed interest in flextensional projectors or various Helmholtz resonators. This is also the case in the field of geophysical exploration, where the specific conditions related to the borehole dimensions and to the harsh environment as well as the use of dipole sources imply the development of specific transducers such as rings or benders. The use of simple models to optimize these types of transducers is difficult, if not impossible. Thus numerical methods such as finite elements or integral equations are needed to reach this goal. The purpose of this paper is first to describe the use of the finite element method to analyze the static, modal, or harmonic behavior of transducers. A brief survey of the theoretical formulation is given while more emphasis is devoted to the modeling conditions. Coupling to integral equations is also discussed. Then, some numerical results obtained for in-air and in-water transducers using the atila code are described and compared with experimental results. Finally, a temperature analysis of the problem related to the modeling of the acoustic wave propagation in the formations is discussed.