An Analytical Approach to Design of Ultrasonic Transducers Considering Lateral Vibrations

The purpose of this paper is to develop a design procedure for Langevin ultrasonic transducers with lateral dimensions larger than a quarter of the longitudinal wave length. In this case, the assumption of the one-dimensional design is not valid, and this method cannot predict the experimental resonance frequency. Some researchers have considered radial and longitudinal normal stresses by means of the apparent elasticity method and reduced the error between the design and experimental resonance frequency. In this research, 3D normal stresses of a transducer’s components i.e. longitudinal, radial and circumferential were considered in the design procedure. The apparent elasticity method was used to modify the elastic modulus and the wave numbers of the transducer‘s components. Resonance lengths of the components were then calculated using the modified values. The design resonance frequency of the transducer was 20kHz. The experimental resonance frequency was measured as 19810Hz. The error of 0.95% between analytical and experimental results showed that the new design procedure can fairly estimate the resonance frequency of the transducer.