THE USE OF THE DISCRETE FOURIER-TRANSFORM TO CALCULATE THE SPATIAL AND TEMPORAL RESPONSE OF LINE-DRIVEN, LAYER-WISE HOMOGENEOUS ACOUSTICALLY LOADED PANELS

A numerical method for evaluating the spatial and temporal response of line-driven, acoustically loaded, damped panels is presented in this paper. Formal solutions to problems of this type are easily obtained using wave-number transform techniques. Here, it is shown that the inversion integral that defines the spatial response may be evaluated efficiently by using the fast Fourier transform algorithm to evaluate the inverse discrete Fourier transform. If desired, the temporal response may then be obtained by performing a further inverse transform. Numerical aspects of the inversion procedure are discussed briefly and guidelines are offered for the selection of spatial and temporal sampling rates and transform lengths. It is then shown that results obtained earlier by using contour integration can also be obtained by using the present technique if the transform parameters are chosen appropriately. The usefulness of the present procedure is then demonstrated through a number of examples. Both the transverse vibration of a water-loaded steel panel and the response of thin, aluminum panels are evaluated in a number of different configurations. In particular, it is demonstrated that the fast Fourier transform approach allows results to be calculated for configurations that are not amenable to classical techniques: e.g., layer-wise homogeneous systems involving a number of parallel elastic panels separated by fluid-filled channels and/or channels filled with porous material.