The objective of the present study is to investigate the combined effects of mechanical shock acceleration pulse as well as non-linear and distributed van der Waals (vdW) attraction on dynamic pull-in instability of electrically actuated nano-cantilevers. To this end, the Euler-Bernoulli beam theory as well as the equivalent mechanical properties of the structure are considered and the non-linear equation of motion is derived. The Galerkin based reduced order modeling together with the fourth-order Runge-Kutta method is employed to solve the non-linear partial differential equation of motion. Using the aforementioned solution, both stable response and unstable one, the so-called dynamic pull-in instability, are taken into account. The model’s predictions for dynamic pull-in voltages are compared with available results in the literature carried out through finite element (FE) method. It is found that the present model can produce high accurate results for normal shock accelerations in comparison to available FE simulations. Furthermore, it is shown that, the present model can remove the incapability of previous models in capturing dynamic pull-in instability for systems subjected to enormous shock accelerations and can be considered as a promising tool for dynamic pull-in analysis of cantilever-type nano electro-mechanical systems (NEMS).

Keywords