Vibration of micro plates in electrostatic fields using Rayleigh-Ritz method

In capacitive type of micromechatronic systems such as microsensors and microactuators the electrostatic forces prove to have a strong influence on the dynamic behavior of the capacitor plate elements in such systems. The present paper focuses on the analysis of the dynamic behavior of micro plates subjected to both electrostatic field and elastic forces. The Rayleigh - Ritz method is applied to obtain an analytical solution of the problem. The displacement function is conveniently chosen to satisfy the geometrical boundary conditions. The electrostatic and the mechanical energy are expressed in terms of the deflection of the plate. Natural frequencies under dynamic conditions are obtained.