A frequency criterion for doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

In general, the vibration frequency of electrically actuated nano/micro-beams under suddenly applied DC voltage is decreased with an increase of the input voltage. However, this descending behavior may be changed, if the initial gap between the movable and fixed electrodes is increased or a large axial compressive residual stress is applied to the system. Accurate determination of the threshold of this frequency behavior change under the van der Waals (vdW) attraction is the objective of the present paper. To this end, a geometric non-linear Euler-Bernoulli electro-mechanical beam model which accounts for the effect of axial residual stresses and the vdW attraction is considered. The oscillatory behavior of the system is studied semi-analytically through the homotopy analysis method (HAM). Employing the HAM solutions, the threshold of the frequency behavior change of the system is obtained. It is found that there exist linear relationships between the normalized parameters of the problem at this threshold. Using this important finding, a frequency criterion for doubly clamped beam-type N/MEMS is introduced. The present findings agree excellently with available experimental and other existing results in the literature as well as those obtained by three-dimensional finite element simulations carried out in COMSOL Multiphysics commercial software.