Modeling and Analysis of Non-Linear Static and Dynamic Pull-in Instabilities of Nanobeams Using Modified Couple Stress Theory

In the nanoscale, the continuity assumption may be violated, and hence, the classical theories, which have been introduced based on the continuity assumption, may lose their accuracy. Therefore, new size-dependent continuum theories are demanded for proper design and analysis of micro/nano-electro-mechanical systems. The aim of the present study is to develop a new non-linear theoretical model, based on the Modified couple stress theory, for analysis of static and dynamic pull-in instabilities of nanobeams, utilized in nano switches. In the present model, the size effect parameter, the fringing field effect, the electro static forces, the intermolecular forces (Casimir and Van der Walls) are taken into account. The non-linear Euler-Bernoulli governing equation of the beam motion and the corresponding boundary conditions are derived by using Hamilton’s principle. The results show that the decrease in the size of the beam increases the beam stiffness. An increase in the fringing field effect, the size effect parameter or decrease in intermolecular forces as well as decrease in the substrate length would increase the ultimate pull-in voltage. Also, when a cantilever nanobeam is affected partially from the free-side end, the effect on the increase of the pull-in parameters of the intermolecular forces and the voltage is greater than that of the nanobeam is affected partially from its support side.