Analytical solution for large amplitude vibrations of microbeams 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 microbeams. Eects of applied voltage and residual axial load on the nonlinear natural frequency and de ection of the microbeams are studied. It shows that pre-compression in microbeams increases the amplitude of de ections for a specic applied voltage. Also, an increase in pre-tension motivates the microbeam 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.