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 o f normal incidence acoustic scattering from a periodically line-suppor ted elastic membrane. A modal series solution exists for this problem. The most slowly convergent part of this solution, the dominant high-r esolution (large wave number) content, is removed from the series repr esentation and summed in closed form in what is called the ANM local s olution. This local solution is represented by a piecewise polynomial that is zero outside of a small region. The remaining part of the solu tion, containing the overall low resolution content, is called the ANM global solution and converges very rapidly. In the present example, t he series representing the global solution falls by three powers of th e index faster than the classical modal solution. The result is an ANM composite (local plus global) solution that requires far less computa tional 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 probl ems. (C) 1997 Acoustical Society of America.