Mathematical Model of the Flextensional Underwater Acoustic Transducer

The basic design principles of the flextensional underwater-acoustic transducer are investigated by developing a mathematical model representation for this type of transducer system, and then establishing the effects that the various geometrical parameters have on the systems performance. The acoustic radiation problem is solved by numerically evaluating the Helmholtz integral for the farfield and nearfield pressure distributions. The mechanical-shell vibration problem is simplified by replacing the continuous shell with an analogous framework consisting of a series of bars and joints and having a finite number of degrees of freedom. Finally, the coupled stack wave equation is solved in terms of an arbitrary terminal impedance that simulates the combined impedance of the shell and acoustic-radiation impedances. Values of transducer impedance, farfield radiation pressures, and effective electromechanical coupling coefficients are calculated and compared with published experimental values for the University of Miami flextensional underwater acoustic transducer. [This research was supported by the U. S. Office of Naval Research, Acoustics Programs.]