Directivity pattern of the sound radiated from axisymmetric stepped plates

For the purpose of optimal design and efficient utilization of the kind of stepped plate radiator in air, in this contribution, an approach for calculation of the directivity pattern of the sound radiated from a stepped plate in flexural vibration with a free edge is developed based on Kirchhoff-Love hypothesis and Rayleigh integral principle. Experimental tests of directivity pattern for a fabricated flat plate and two fabricated plates with one and two step radiators were carried out. It shows that the configuration of the measured directivity patterns by the proposed analytic approach is similar to those of the calculated approach. Comparison of the agreement between the calculated directivity pattern of a stepped plate and its corresponding theoretical piston show that the former radiator is equivalent to the latter, and the diffraction field generated by the unbaffled upper surface may be small. It also shows that the directivity pattern of a stepped radiator is independent of the metallic material but dependent on the thickness of base plate and resonant frequency. The thicker the thickness of base plate, the more directive the radiation is. The proposed analytic approach in this work may be adopted for any other plates with multi-steps.