PARAMETRIC OSCILLATIONS OF A MEMBRANE IN AN ALTERNATING ELECTRIC-FIELD

Axisymmetric oscillations of a circular conducting elastic membrane placed between the grounded plates of a capacitor and subjected to the action of an alternating voltage are investigated. Approximate expressions are obtained in the quasistationary approximation of the equations of electrodynamics for the potential of the electric field between the plates and a self-consistent integro-partial differential equation in the oscillations of the membrane. A solution of the corresponding boundary-value problem is constructed and a qualitative analysis of the parametrically excited oscillations is carried out. The conditions for stability and instability of the natural oscillations of different modes are obtained in terms of the electromechanical parameters.