### ASA 124th Meeting New Orleans 1992 October

## 3aSA9. Approximations for the 2-D Green's function of a fluid-loaded
plate.

**Douglas M. Photiadis
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*Naval Res. Lab., Washington, DC 20375-5000
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Simple analytical formulas to predict the acoustic component of the 2-D
Green's function of a fluid-loaded plate are presented. The formulas do not
require any side computations such as numerical zero finding or numerical
integrations. The simplest result obtained provides a good estimate of the
Green's function for a very broad range of frequencies, being degraded only
near the coincidence frequency. A somewhat more complicated formula, almost
uniformly valid in frequency, and yielding reasonable accuracy even at
coincidence, is also presented. Numerical results comparing the asymptotic
approximations to the ``exact'' Green's function are presented, and show
significant improvement over a basic steepest descents-based approximation. For
large values of x, very high accuracy can be achieved with relative errors of
less than 0.1%. For other less stringent applications, the approximations are
accurate to within 10% at fairly small distances from the source, requiring
only k[sub f]x>1 and k[sub 0]x>0.5.