Computationally efficient modeling of structural inhomogeneities by analytical/numerical matching

Abstract

Solving structural acoustic problems in the mid-frequency range is a challenging task. Computation is expensive due to both the large well-coupled nature of the domain and resolution constraints such as small flexural wavelength. In addition, discrete structural elements such as ribs and stiffeners cause localized high-resolution content that requires much greater resolution than would be otherwise warranted. A method called analytical/numerical matching (ANM) alleviates this additional computational burden. The ANM method captures the particular influence of the inhomogeneity on the structure in an analytically expressed local solution. The governing equation is then used to show that the extraction of this local solution by superposition amounts to replacing the original discrete influence of the inhomogeneity by a smoothed forcing derived from the local solution. The result is a smoother problem that can be computed more efficiently and without the loss of any information. The method has been demonstrated for several configurations of increasing complexity in the process of its development as a useful tool for efficiently solving realistic problems of engineering interest. These problems have shown the usefulness, accuracy, and efficiency of the method. Examples will be presented, including recent work on implementation within a finite element analysis.