Parametric Coupling in a Nonlinear Electromechanical System

Parametric coupling that arises under certain conditions of excitation has been analyzed in an electrical R-L-C circuit that is coupled with a mechanical system through a nonlinear inductance. It is found that high frequency excitation of the electrical circuit can support low frequency oscillation of the mechanical system, the entire process arising through the existence of a low order instability in the coupled system. Approximate methods of analysis are used to show the existence of the instability as well as the form of subsequent motion, and their numerical results are compared with analog computer results. The behavior of the electromechanical system can be shown to be analogous to a similar coupling that can occur between lateral wall vibrations and free surface oscillations of liquid in a partially filled elastic cylinder.