Using Parameter Expansion Method and Min-Max Approach for the Analytical Investigation of Vibrating Micro-Beams Pre-Deformed by an Electric Field

Two powerful analytical methods called Parameter Expansion method (PEM) and Min-Max approach (MMA) are used to obtain the analytical solution of micro-beams actuated by an electric field. The nonlinear equation of motion has both even and odd nonlinearities. It is shown that two terms in series expansions of PEM are adequate to achieve a highly accurate solution of mentioned system. Comparison of the obtained solutions using numerical method shows the accuracy of the analytical procedures. It is proved that the approximated solutions using PEM are in more agreement with numerical results in comparison with MMA.