Effects of driving frequency of longitudinal transducer on the vibration characteristics of a stepped plate

The flexural vibration characteristics of a stepped plate, driven at its center by different frequency of longitudinal transducer with a certain area are investigated. The variation in the nodal circle, fundamental frequency and displacement distribution of the stepped plate are calculated by using finite element method (FEM) under different driving frequencies. The results show that the fundamental frequency and nodal circle of the flexural-vibration stepped plate (FVSP) increase with an increase in the driving frequency of the longitudinal vibration ultrasonic transducer (LVUT), before the second-order flexural vibration occurs. When the driving frequency is f = 28 kHz, the displacement amplitude of the stepped plate can achieve the maximum, and the nodal circle radius of the stepped plate is 2.61 cm which fits evenly the edge of stepped profile. Meanwhile, the directivity and radiation efficiency of the FVSP would be greatly improved in a special driving frequency. The conclusions agree with the experimental ones and are significant for both design and applications of the stepped plate.