Directivity pattern of the sound radiated from square stepped-plate radiators

A square flat-plate radiator driven by a longitudinal vibrator at the resonant frequency of its fourth-order natural vibration mode at its center for the generation of highly directional ultrasonic radiation in air is studied herein. The radiator was able to create a bending vibration mode whose four straight nodal lines were located at a 45° angle on each side. To obtain highly directional sound, the surrounding area of the four right isosceles triangles formed by a nodal line and two sides is modified to be raised one by half the wavelength of sound radiated in the propagation medium so that surface elements vibrate in phase. Then, the relation among the frequencies, nodal lines of the rhombus mode, and geometrical dimensions of the radiator is determined. The calculated directivity pattern of the stepped-plate radiator is equivalent to that of its corresponding theoretical piston, i.e., a stepped plate is a piston-like radiator. Results show that the measured vibrational-mode shape of the stepped-plate radiator is consistent with the calculated one, and the calculated directivity pattern is almost similar to the measured one.