Analytical Solution for Large amplitude Vibrations of Micro-beams Actuated by an Electro-static Force

An analytical study using Variational Iteration Method (VIM) is carried out in order to investigate the vibrations of electro-statically actuated double-clamped and simply-supported micro-beams. Effects of applied voltage and residual axial load on the nonlinear natural frequency and deflection of the micro-beams are studied. It shows that pre-compression in micro-beams increases the amplitude of deflections for a specific applied voltage. Also, an increase in pre-tension motivates the micro-beam to show more nonlinear behavior in an applied voltage. Predicted results are compared with the experimental data available in the literature and also with numerical results which shows a good agreement. It is concluded that the second order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes.