Equivalent circuit of the two-dimensional vibration direction converter in coupled vibration

With the features of transmitting energy from multiple directions to one direction and transmitting vibrations from one source in multiple directions, the two-dimensional vibration direction converter has important applications in power ultrasonic technology. However, for the complexity of using the wave equation to design and analysis the two- dimensional vibration direction converter, a concise equivalent circuit for the converter is investigated in this work. By introducing a two-dimensional mechanical coupling coefficient and a longitudinal force transform coefficient, and based on the electromechanical analogy principle, the equivalent circuit and resonance frequency equation of the two-dimensional vibration direction converter vibrating in anti-phase and in-phase two-dimensional coupled vibration is deduced. The resonance frequencies of two two.dimensional vibration direction converters consisted of two different materials are calculated by using the proposed frequency equation, which are in agreement with the results from the finite element method and the experimental test. It provides a concise method for the design and applications of such ultrasonic vibration system.