APPROXIMATE EVALUATION OF THE SPECTRAL DENSITY INTEGRAL FOR A LARGE PLANAR ARRAY OF RECTANGULAR SENSORS EXCITED BY TURBULENT-FLOW

An approximate numerical procedure has been developed for rapidly eval uating the spectral density integral that predicts the output of a pla nar array of many sensors excited by turbulent boundary layer pressure fluctuations. This procedure is particularly useful in cases where th e transfer function factor of the integrand is not a simple function o f the wave numbers in the flow and transverse directions. The procedur e exploits the facts that the entire integrand is a separable function of these two wave numbers and, when the number of sensors is large, t he array function factor of the integrand is a rapidly varying functio n of wave number, characterized by many similar shaped lobes. In addit ion, a model for multilayered media is employed to provide the transfe r function for boundary conditions that closely correspond to reality. Results generated by this procedure were compared to those from an ex act evaluation of the integral which is possible if the transfer funct ion is taken to be constant; there was agreement to within 0.2 dB or b etter over a broad frequency interval. Some results for a realistic tr ansfer function are presented, such as the case of an elastomeric laye r backed by an elastic plate with the sensors embedded at an arbitrary position within the layer.