### ASA 125th Meeting Ottawa 1993 May

## 2aEA1. Approximate evaluation of the spectral density integral for a large
planar array of rectangular sensors excited by turbulent flow.

**William Thompson, Jr.
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*Dept. of Eng. Sci. & Mech. and Appl. Res. Lab., Penn State Univ., P.O. Box
30, State College, PA 16804
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**Robert E. Montgomery
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*Naval Research Lab., Orlando, FL 32856-8337
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An approximate numerical procedure has been developed for rapidly
evaluating the spectral density integral that predicts the output of a planar
array of sensors excited by turbulent boundary layer pressure fluctuations.
This procedure is particularly useful in cases where the transfer function
factor of the integrand is not a simple function of the wave numbers in the
flow and transverse directions. The procedure exploits the facts that the
entire integrand is a separable function of these two wave numbers and, for
large arrays, the array function factor of the integrand is a rapidly varying
function of wave number, characterized by many similar-shaped lobes. In
addition, a model for multilayered media is employed to provide the transfer
function for boundary conditions that closely correspond to reality. Results
generated by this procedure were compared to those from an exact evaluation of
the integral that is possible if the transfer function is taken to be constant;
there was agreement to within 0.2 dB or better over a broad frequency interval.
Some results for a realistic transfer function are presented, such as the case
of an elastomeric layer backed by an elastic plate with the sensors embedded at
an arbitrary position within the layer. [Work supported by NAVSEASYSCOM 06UR.]