With the highfrequency transducer is high, it can obtain sharp directivity, that is helpful for sonar systems to identify the kind and shape of underwater fine targets. In recent years, lots of new materials have already been applied in the field of underwater acoustic highfrequency transducers, but piezoelectric ceramics are Tromethamine (hydrochloride) Technical Information Nonetheless the mainstream supplies. Piezoelectric transducers with piezoelectric ceramic as the functional material have greater reliability, impact resistance and longtime operating stability than versatile sensors. It really is the mainstream device of underwater acoustic systems [2]. The thickness vibration mode is definitely the dominant working mode for highfrequency transducers. Because the resonance frequency in the thickness vibration mode is relatively higher, the coupling effect is frequent in highfrequency transducers. For disc piezoelectric ceramics, it truly is hard to get an ideal thickness vibration mode. Changing piezoelectric sample sizes can weaken the coupling effect. Nonetheless, the sample size was commonly fixed. On the one hand, the coupling reverses the vibration displacement on the piezoelectric vibrator surface, top to decrease in the transmission efficiency with the transducer. Alternatively, the coupling causes many indistinguishable resonance peaks to appear near the thickness vibration frequency. Furthermore, coupling makes the resonance frequency, impedance characteristics and other important parameters from the transducer much less consistent. It makes the transducer hard to design to acquire high yield. A lot of transducer experts have had substantial discussions on highfrequency broadband transducers [6,7]. Onedimensional vibration theory was generally employed to approximate the thickness vibration of ideal piezoelectric discs, even though radial coupling should be considered for finitesize piezoelectric discs [8]. As early as 1977, Mori et al. proposed thePublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.Copyright: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is definitely an open access post distributed under the terms and conditions of the Inventive Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ four.0/).Actuators 2021, ten, 226. https://doi.org/10.3390/acthttps://www.mdpi.com/journal/actuatorsActuators 2021, ten,two ofapparent elasticity approach to take care of the coupling vibration of piezoelectric vibrators [9]. Lin Shuyu, et al. introduced the equivalent elastic coefficient into the coupled vibration of piezoelectric disc plates and rings by an analytical strategy, and derived the equivalent circuit and resonance frequency equation of multimode coupled vibration of piezoelectric ceramic vibrators [10,11], Li Mingxuan et al. also analyzed the tension voltage characteristics of the highfrequency thickness mode transducer, and gave the traits of highfrequency oscillation below distinctive loads [12]. In addition to the theoretical Diloxanide manufacturer calculation research, the finite element simulation process was also employed to investigate the coupling impact. Guo N., Kocbach J. and Lee P. used the finite element approach and numerical analysis system to analyze the coupled vibration modes of piezoelectric oscillators, and calculated the secondorder theory of transversely coupled longitudinal vibration piezoelectric crystals [135]. D. Kybartas et al. applied the finite element process to analyze the electromechanical coupling coefficient of every order vibrat.