Accuracy of infinite elements in structural acoustics modeling

Abstract

Infinite elements are used in conjunction with finite elements to solve a number of structural‐acoustics problems. When finite elements alone are used to model an infinite fluid domain, a truncation of the model is necessary at a “sufficiently large” distance from the area of interest. In addition, steady state problems require the imposition of a boundary condition to absorb outgoing waves. A common practice in fluid‐structure interaction problems is to model approximately one‐and‐a‐half acoustic wavelengths of external fluid and to impose a plane‐wave absorbing boundary condition. Although workable, this approach can result in very large models that are costly to solve. An alternate way to treat the infinite domain and significantly reduce the number of equations is by using infinite elements [e.g., P. Bettess, Int. J. Numer. Methods, Eng. 11, 53–64 (1977)] alone, or in conjunction with finite elements. This is possible because infinite element shape functions contain terms that describe an outward traveling and exponentially decaying wave. The derivation of the element is reviewed and its accuracy in problems involving infinite cyclinders is presented. Results from two‐dimensional scattering off rigid and elastic cylinders are compared to theoretical and previously published results. The fluid impedance for waves on a cylindrical boundary is also calculated and compared with closed form solutions. In all instances considered, accurate answers were obtained with the use of no more than two layers of finite elements, plus a layer of infinite elements. In many instances, the infinite elements alone produced excellent results.