The application of analytical/numerical matching to structural discontinuities in structural/acoustic problems

Analytical/numerical matching (ANM) is introduced to more efficiently model structural discontinuities in structural/acoustic problems. The general method is explained in detail for the simple example problem of normal incidence acoustic scattering from a periodically line-supported elastic membrane. A modal series solution exists for this problem. The most slowly convergent part of this solution, the dominant high-resolution (large wave number) content, is removed from the series representation and summed in closed form in what is called the ANM local solution. This local solution is represented by a piecewise polynomial that is zero outside of a small region. The remaining part of the solution, containing the overall low resolution content, is called the ANM global solution and converges very rapidly. In the present example, the series representing the global solution falls by three powers of the index faster than the classical modal solution. The result is an ANM composite (local plus global) solution that requires far less computational effort to resolve. In addition to providing a clear abstraction of the method, the example problem allows the equivalence of the ANM solution to be verified, and indicates the importance of resolving the fine scale effects of discontinuities in constrained scattering problems.