Study On The Vibration And Radiation Characteristics Of Stepped Circular Plates In Longitudinal-Flexural Airborne Transducer

The compound transducer consisting of a longitudinal vibrator and a flexural circular plate combines the high energy and efficiency of the former and the low impendence and wide spreading scale of the latter. It is now widely used in aerosol particle precipitation, ultrasonic atomization and ultrasonic detection. But to circular plate with large surface area, the vibrate modes generated is often so high that there is reverse phases existing, which result in a decrease in radiation impedance, electric-acoustic efficiency and the electric power, as well as poor directivity. So a stepped circular plate is adopted which can compensate the phase by different thickness. However, the theory about it is still scarce. Or if there is some, they usually introduce large approximation so it is difficult to be used in practical design. In this article based on vibration theory of the flexural plate, the frequency equation, the equivalent mass and radiation impedance are derived and further, design theory is introduced. After the nonlinear and absorption effect is taken into account in the applications where high power ultrasonic is involved, the first and second harmonic components of the sound field of stepped circular plate is analyzed, based on the KZK equation and quasi-linear condition. Moreover, taking on the Rayleigh integral the far field acoustic pressure and the directivity formula is obtained. The measured results are in good agreement with this theoretical value.In detail, the context include several aspects:1. According to several boundary conditions, the frequency equation of flexural circular plate is calculated. Similarly some coefficients in the displacement distribution can also be acquired, which provide a preparation for further study.2.To the circular plate working in axial symmetry vibration at resonant frequency, the equivalent mass in analytical form is derived, that's is, , and further, the equivalent compliance is obtained using the formula C = 1l 2 M . The radiation impedance at the resonant frequency, inanalytical form, is Consequently, theequivalent circuit of the plate is obtained.3. When the number of the nodal circles and the design frequency are given, the stepped circular plate satisfying the requirement can be designed. The stepped plate designed in this method can overcome the limitation of the sound field generated by circular flat.4.According the Rayleigh integral, the far field of this kind of plate is resolved,namely, . And the formula as a far field directivity function is assumed to be useful in analyzing the axis-symmetry sound field.