The Directional Characteristics of a Free-Edge Disk Mounted in a Flat Baffle or in a Parabolic Horn

Abstract

In the attempt to obtain a sharp beam of supersonic sound from a parabolic horn, it became apparent that the sharpness of the beam was a function of the mode of vibration of the diaphragm exciting the horn. Experiments showed that the sharpest beams with the smallest side lobes were obtained when the diaphragm was radiating most of the energy toward the side walls of the horn rather than toward the mouth. Experiments with a free-edge disk for a diaphragm connected the wide angle radiation with the two nodal circle mode of vibration of the disk. Comparison between directional patterns measured with the disk in a flat baffle and calculated patterns confirmed the correlation between the wide angle radiation and the two nodal circle mode. Further analysis indicated that similar radiation patterns could also be obtained from one and three nodal circle modes of vibration. In the analysis, the differential equation for the vibration of a thin plate is solved for a free-edge circular disk assuming circular symmetry and considering a driving force applied at an arbitrary circle concentric with the disk. The dynamic curve of the disk is given for any frequency in the form of a series of the normal modes of the disk, and the directional pattern of the radiation from the disk mounted in an infinite baffle is calculated. The calculations have been so systematized and tabulated that the dynamic curve and directional pattern for any disk and frequency can be calculated quite readily. The analysis is sufficient to predict the disk diameter and thickness required for the one, two, or three nodal circle modes and for any frequency, when the disk is mounted in a flat baffle and when the maximum radiation is placed at an arbitrary angle from the axis. On the basis of the analytical predictions, a disk has been made to give the wide angle radiation required with the disk vibrating with one nodal circle instead of two nodal circles as discovered experimentally.