Theoretical study on resonance frequencies of the vibration modes of Janus–Helmholtz transducer

Janus-Helmholtz transducer has the characteristics of high-power and broadband transmission due to the coupling between the longitudinal resonance of the driver and the liquid cavity resonance of Helmholtz resonator. Traditional view holds that the low frequency resonance peak in the transmitting voltage response curve in water is fluid cavity mode of Helmholtz resonator while the high frequency resonance is the longitudinal mode of Janus transducer. However, in the past few decades, a large number of experimental studies have found that this conclusion is questionable. This work is to distinguish the two resonances in the response curve and the two vibration modes of Janus-Helmholtz transducer. Based on the Janus-Helmholtz transducer prototype reported in the literature, the resonance frequencies of the vibration modes of Janus-Helmholtz transducer are studied theoretically. The structure dimensions and material parameters of the prototype are listed in detail. The test results and simulation results of conductivity are also presented. The longitudinal resonance of the driver is determined by using the equivalent circuit method and finite element analysis. Radiation masses of both Janus transducer and typical longitudinal vibration transducer are also calculated to analyze the phenomenon of the sharp decrease of longitudinal resonance frequency in water. Acoustic modal analysis by using ANSYS software is performed to investigate the resonance frequency of complex Helmholtz resonator in Janus-Helmholtz transducer. Correction length on the vent introduced by external fluid sound radiation is used to obtain the accurate Helmholtz resonance frequency. The sound pressure distribution of Helmholtz resonator obtained through finite element method is investigated, and the correct equivalent formula for solving the Helmholtz resonance frequency is obtained. The results reveal that the first resonance in the response curve is driver resonance while the second one is Helmholtz resonance, which is contrary to the traditional view. The considerable reduction of driver resonance frequency in water is mainly due to the large radiation mass on the four large radiation surfaces of the Janus transducer, which also causes the sharp response of driver resonance. In Janus-Helmholtz transducer, there are two Helmholtz resonators with the same size, instead of only one resonator in the traditional view. The two resonance frequencies solved by the method proposed in this work are in good agreement with the test and simulation results. These conclusions play an important role in correctly understanding the structure and characteristics of Janus-Helmholtz transducer at source, as well as provide technical support for structural optimization and innovation, thus improving the acoustic emission properties of the transducer.