Velocity control and the mechanical impedance of single degree of freedom electromechanical vibrators

Most of the transducer devices used in present day sonar arrays are usefully approximated as single degree of freedom devices. Such devices exhibit a minimum in their mechanical input impedance to their radiating face at the fundamental resonance frequency. This minimum in impedance, leading to possible wide fluctuations in velocity across the array, can result in deterioration of electroacoustic performance and possibly disastrous results to hardware if left unchecked. The standard technique used to prevent this is attributed to D. L. Carson [J. Acoust. Soc. Am. 34, 1191–1196 (1962)] and essentially provides an electrically induced antiresonance near the mechanical resonance frequency. It is shown that this technique results in two minima, one residing on each side of the previous minimum. The resulting bandwidth over which velocity control of the array can be achieved is closely tied to the bandwidth between these minima. The relative locations of these minima are dependent only on effective electromechanical coupling coefficients and the ratio of the electrical antiresonance to mechanical resonance frequencies. This bandwidth appears to have a practical limit of approximately an octave.