The Design Of Multi-stage Bending Vibration Disc

Air medium is different from solid medium in spreading high-power sound waves. The low acoustic impedance of air medium makes the traditional air interface high-power ultrasonic transducer has serious impedance mismatches problem. Therefore, the application of ultrasonic power in air has been limited.By the flexure vibration radiation plate and the longitudinal vibration transducer with a combination of radiator, because of which low acoustic impedance of flexure vibration and the characteristics of the high radiation efficiency of longitudinal vibration, which has a good application in power ultrasonic field with air interface.The front radiation board of radiator in flexural vibrators will emerge the anti-phase region on both sides of the nodal line. It will influence the radiation efficiency of sound field. In order to overcome destructively interfere of anti-phase region, front radiation board of the complex vibration transducer will be designed to be stepped plate (Thickness is equal to half wavelength of air medium). In practical application, in order to get the big radiated acoustic power, usually choose multiple stepped plates as the front of the transducer radiation board. The stepped plate design is to solve the design parameters from the frequency equation of stepped plate. But the frequency equation of stepped plate contains special functions and the equation number is so much that general numerical calculation method is difficult to solve. This paper take the flexure vibration stepped plate with three steps and Free boundary as an example and puts forward the method of solve design parameters from the frequency equation of stepped plate in the determination of the flexure vibration frequency, basal thickness and the material parameters of stepped plate. And that, apply this method to stepped plate with single step and stepped plate with double steps, calculated the radius and section line radius in the different frequencies. Through the contrast the calculation results of stepped plate, base plate and flat plate which thickness is equal to central part of stepped plate found law, summing rules, Provides a method for stepped plate with multiply steps.The specific works are as follows:(1)On the basis of thin plate flexure vibration and circular plate flexure vibration, derived the displacement equation and the frequency equation of the stepped circular plate with three steps in free-border conditions.(2) Through programming solve the value of radius and nodal radius from the flexure vibration frequency equation of stepped circular plate with three steps. Calculation of a group of stepped plate with three steps at different frequency by finite element, and comparing the calculation results. The result is consistent with the theoretical calculation, and that, the formation is accord with bending vibration formations.(3) Using the above design method for solving value of radius and nodal radius of stepped circular plate with single step and stepped circular plate with double steps at the different frequency. Through the contrast the calculation results of stepped plate, base plate and flat plate which thickness is equal to central part of stepped plate found that radius value of stepped circular plate is close to response of flat plate which thickness is equal to central part of stepped plate in the same frequency, free-border condition.Setting the radius value of stepped plate to response radius of flat plate which thickness is equal to central part of stepped plate. That is to say α=α中Recalculate nodal radius value again after optimization radius. Finally, recalculate the parameters of stepped plate by finite element after radius optimization settings.The calculation results show that the optimization the radius of the stepped plate set design method. It will become simple when using numerical method for solving frequency equation after initial value optimization settings. The calculation speed will increase, the calculation precision can also improved, which greatly reduces the difficulty of design the stepped plate in flexural vibration(4) Processed a stepped plate with double steps and a stepped plate with three steps, and tested its resonant frequency and vibration mode curve.