Design of Ultrasonic Transducer for Secondary Wave Generations with High Directivity

In this paper, we described a method of designing ultrasonic transducer which simultaneously radiates two finiteamplitude ultrasonic waves to produce the secondary waves with high directivity. For nonlinear effects, it is necessary that the frequencies of two primary waves are coincident with natural frequencies of the ultrasonic transducer. The main problem here is to predict the resonance frequencies of the first mode as well as higher modes. While the first resonance frequency of the transducer can be estimated easily, it is not trivial to do higher ones. When the length of transducer is much greater than its diameter, this problem is reduced to one-dimensional and higher mode frequencies are nothing but multiples of the first mode frequency. However, such a case is seldom encountered. Using the transfer matrix method, we obtained the resonance frequencies of the transducer analytically and compared these with numerical results from the simulation. The theoretical and simulation results are in good agreement with the difference of 3–6kHz.