A Method for High-Speed Calculation of the Exact Solution for the Pressure in the Nearfield of a Circular Baffled Piston

Abstract

A high-speed method has been developed for calculating from the exact integral solution the pressure at each point in the nearfield of a sinusoidally excited circular piston in an infinite baffle. Previously the exact nearfield pressure has been calculated by means of a double numerical integration over all source points on the piston face. The phase of the signal arriving at a field point from each point on the piston must be taken into account precisely. One investigation in which the double integration was employed is that of Zemanek, who published three-dimensional and contour plots of data obtained by this method [J. Acoust. Soc. Amer. 49, 181–191 (1971)]. We have reduced the calculation to a single numerical integration by starting with the known exact solution for the field produced by impulse motion of the piston. For each field point, we compute, at the frequency of interest, the Fourier transform of the impulse response. Thus, we obtain the transfer function, a complex quantity that, when expressed in polar form, gives us the amplitude and phase of the pressure variation. We have made three-dimensional and contour plots that compare favorably with those published by Zemanek. The high speed of our method makes possible the efficient calculation of the difference frequency source function. (See J. G. Willette, Paper F9 of this meeting.) [This work was sponsored by the Office of Naval Research.]