Application of the finite element method to two-dimensional radiation problems

Abstract

Acoustic fields radiated by vibrating elastic bodies immersed in an infinite fluid domain are, in general, quite difficult to compute. This paper demonstrates in the two-dimensional (2-D) case that the radiated near field can be easily obtained using the finite element method if dipolar damping elements are attached to the mesh external circular boundary. These elements are specifically designed to absorb completely the first two components of the asymptotic expansion of the radiated field. Then, the paper provides a new extrapolation method to compute far-field pressures from near-field pressures, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition. These developments are valid for any radiation problem in 2D. Finally, two test examples are described, the oscillating cylinder of order m and a finite width planar source mounted in a rigid or a soft baffle. This approach is the generalization to 2-D problems of a previously described approach devoted to axisymmetrical and three-dimensional (3-D) problems [R. Bossut et al., J. Acoust. Soc. Am. 86, 1234–1244 (1989)]. It has been implemented in the ATILA code. It is well suited to the modeling of high-frequency transducers for imaging and nondestructive testing.