Design of Sandwich Transducer Based on the Equivalent Length Algorithm

The sandwich transducer structure is comprised of three components along its main axis: the back metal cap, piezoelectric ceramic stack and the horn. The purpose of this work is to present a simplified method, referred as the equivalent length algorithm, to design the actuator parameters including each segment length and the resonance frequency f_s. The actuator length L and the propagation wavelength λ along its main axis satisfy the standing wave theory. So, define an equivalent length coefficient for each part of the actuator, and then the sandwich structure is regarded as a single material cylindrical rod with equivalent length L′. According to the standing wave theory, the equivalent length L′ of the actuator can be determined with the given resonance frequency f_s, or vice versa. The phase length of each part of the actuator in the standing wave is optimized freely in the design procedure. The actual length of each part of the actuator is determined by the equivalent length coefficient. Finally, the resonance frequencies of three given actuators are calculated with this method. They are compared with those obtained through Ansys simulation and those measured by an impedance analyzer. The results show agreement.