Study On Radiation Impedance And Sound Field Of The Flat And Stepped Circular Plates In Flexural Vibration

The use of high power ultrasonics in gases has increased with the development of ultrasonic technique such as ultrasonic levitation, drying, agglomeration, aerosol particle precipitation and gauging. The main problems concerning the ultrasonic generation and propagation in gases are the low acoustic impedance and the high absorption of the medium. In order to obtain efficient transmission of ultrasonic energy in gases it is necessary to produce high directivity and achieve a good impedance match between the transducer and the gases. The compound air-coupled transducer consisting of a sandwich longitudinal piezoelectric vibrator and a circular thin plate in flexural vibration has the advantages of large radiation surface and improved impedance matching and has used in producing ultrasound of high directivity in air.In this paper, the radiation impedance and sound field of the flat and stepped circular plates in flexural vibration as an ultrasonic radiator are studied. The originality innovation and research results include several aspects as following:1. Calculation for radiation impedance of the fiat circular plate in flexural vibrationThe nodal circle radius and frequency equation and its roots are discussed based on analyzing the vibration characteristics of the circular thin plate. The expressions for radiation impedance of the flexural circular plate in three different boundary conditions are derived. The values of radiation impedance for six vibration modes are calculated by using high precision numerical method of integration, Gauss quadrature formula. The curves of resistance and reactance varying with ka are plotted.Radiation impedance is not only the function of the wave number k and the radius a, but also concerned with the number of nodal circle (vibration mode). The values of resistance and reactance decrease with the number of nodal circle increasing, and the larger the number of nodal circle is, the less the values of resistance and reactance are. When the flexural plates are in different boundary conditions, the values of resistance and reactance are different although they are in the same vibration modes. The fewer nodal circles is, the values of radiation impedance of the flexural circle plate with free edge are lest, the values of circle plate with simple supported edge are largest, and the values, with fixed boundary, are middle. The more nodal circles are, the difference of the values of radiation impedance of the flexural circle plates in three different boundary conditions is slight.2. Study on sound field of the stepped circular plate in flexural vibrationThe radiation ultrasonic field of circular plate with stepped thickness is analyzed, the acoustic pressure in the far field is obtained and the directivity function is derived theoretically. The directivity pattern is plotted by programming.The directivity of stepped plate has improved a lot than the flat plate. The theoretical directivity pattern is in good agreement with the measured result of Gallego.3. Calculation method of radiation impedance of flexural stepped plateAs far as the radiation impedance of stepped circular plate is concerned, the classical theory has difficulty in calculation because the radiation surface is not colaner. A new calculation method is put forward from the superposition theory of power.4. Calculation for radiation impedance of flexural stepped plate with one stepThe values of radiation impedance of stepped plate with one step in three different boundary conditions are calculated by using numerical method of integration from the calculation method introduced above.The radiation impedance of stepped plate with one step is the function of the wave number k and the radius a, the resistance is greater and the reactance is smaller in the higher frequency than in the lower frequency. The values of resistance and reactance of the one-stepped plate in free boundary condition are larger than those of the flat plate in the first vibration mode when the values of ka are the same. The values of resistance and reactance of the one-stepped plate in simple supported and fixed boundary conditions are larger than those of the flat plate in the second vibration mode when the values of ka are the same, respectively.These provide the scientific theoretical foundation for utilizing these types of vibrators intentionally and efficiently in practical applications.