Investigation of the nonlinear phenomena of a Langevin ultrasonic transducer caused by high applied voltage

In the field of power ultrasound, Langevin ultrasonic transducers (LUTs) usually operate at a large displacements output power by applying high voltages. However, empirically, a LUT exhibits nonlinearities such as amplitude jumping and peak hysteresis for high voltages in actual operations. The nonlinearities would reduce the efficiency and output accuracy of an LUT. In this research, the burst-mode method was used to measure the longitudinal vibration velocity of the LUT, which gradually decreased with time after the excitation voltage was turned off. The equivalent mechanical losses and equivalent spring constants were determined using the velocity attenuation rate and resonant frequency and they were found to be the linear functions of velocity, helping to develop a novel nonlinear model. This model contained two quadratic nonlinear terms based on the linear model. Furthermore, the developed nonlinear model was analyzed using the Lagrangian method as well as the multiscale method, which confirmed that the model was effective in describing the nonlinear behavior. It was also found that the frequency-amplitude curve bent when the nonlinear term was taken into account, which resembled the nonlinear phenomenon tested experimentally. From a physical point of view, this bending was meaningful because it led to the formation of multi-valued response regions with jumping phenomena. Additionally, according to the obtained results, the maximum value of the system response was independent of the degree of nonlinearity of the system.