Dynamic Mechanical Stability in the Variable-Reluctance and Electrostatic Transducers

Abstract

Large displacement behavior of the variable-reluctance, and the mathematically equivalent electrostatic, transducing mechanism was analyzed in order to evaluate the importance of mechanical instability as a limiting factor in high-power sound projectors. Previous work by Hunt et al. had shown the existence of static instability. This paper first considers the effect of transients on static stability and then shows that instability can also occur under steady-state dynamic conditions, even when the system is statically stable. When the excitation is increased in order to increase the amplitude of the oscillations, the average displacement also increases, which leads to collapse of the gap. This interdependence of the oscillatory motion and the average displacement, intentionally excluded from linearized treatments, is the cause of dynamic instability. Detailed calculations show the conditions for instability for typical values of mechanical Q, polarization, and frequency. Under steady-state dynamic conditions, the average displacement can exceed the static limit of 13 the gap length, and the relative oscillatory displacement amplitude can reach 12 or more without collapse. Although such instability renders the transducer inoperative, the calculations indicate that it will seldom be a serious limitation.