Analysis of a flextensional transducer using piece-part equivalent circuit models: determination of the shell contribution

The electromechanical behavior of the class IV flextensional transducers involves a complex coupling between the longitudinal vibration of the piezoelectric or magnetostrictive driver and the flexural motion of the shell. It is nevertheless amenable to equivalent circuit modeling. Such an equivalent circuit can be obtained by assembling the equivalent circuits characterizing the driver and the shell, using the following assumptions: the driver is described using one motional branch corresponding to its first longitudinal mode, the shell is described using two motional branches, the first one related to the first flexural mode, the second to the second flexural, or membrane mode. The aim of this paper is to develop an analytical solution for the first two flexural modes and the mechanical antiresonance frequency of the shell