Modeling and Dynamic Behavior of Electrostatic Tranducers with Distributed Parameters

Abstract

The dynamics of an electrostatic transducer as a 2-field system with distributed parameters is studied, here in form of a 1-dimensional capacitor composed of a flexible strip with clamped ends and a rigid plate opposite including inductance and resistance effects. Both electrical and mechanical input signals are taken into consideration, and the influence on the electrical charge between the plates as well the relative displacement of the plates is discussed indetail. First, a formulation of the governing non-linear boundary value problem is presented. Next the simplified time-independent boundary value problem is derived when only a polarization DC voltage is applied. Then, the equations of motion describing the dynamic behavior of the transducer in the neighborhood of the steady state are generated. The RITZ method for discretization is introduced to obtain simplified equation sets for approximate solutions. Starting with the roughest 1-term truncation for both displacement and charge to be interpreted as the classical lumped-parameter transducer, the discussion is finally generalized studying truncations of higher order.