Electrical equivalent circuit of loaded thick Langevin flexural transducer

In this paper, an electrical equivalent circuit of a loaded thick Langevin flexural transducer is proposed. As there are two vibration components at the mechanical output terminal of a thick flexural transducer, that is, lateral and rotational components. A load, corresponding to each vibration component, applied to the transducer must also be considered separately. When it is assumed that the load is fluid and that the mechanical output port is the end surface of the flexural transducer, the rotary motion of the end surface only contributes to sound radiation into fluid. An analytical solution of Timoshenko's beam theory given by Miklowitz and the piezoelectric equation are applied to calculate the free vibration mode and the electrical equivalent components of transducer. Using this derived equivalent circuit, the behavior of the loaded flexural transducer is experimentally studied to prove the validity of the proposed circuit.