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The van der Waals ( vdW ) force, along with the electrostatic force and the first-order fringing field effect, act on the electrostatically actuated nano-cantilever ( EANC ) when the gap between the deformable electrode and the stationary electrode is less than 20 nanometres. Because of the  vdW  force, the  EANC  can undergo a pull-in phenomenon even without the electrostatic force when the nano-cantilever length exceeds its detachment length. The  vdW  force also results in a significant reduction in static pull-in instability parameters of the slender  EANC  compared to corresponding parameters obtained when this force is absent. This paper aims to augment the stable static travel range ( i.e.,  the pull-in displacement) of the aforementioned  EANC  having a length close to its detachment length by varying the beam width. The beam width is assumed to vary in linear and parabolic manners and is controlled using a width variation parameter in each case. The governing equation of the Bernoulli-Euler beam theory and the Galerkin’s technique are utilised to obtain the weighted residual statement ( GWRS ). The  GWRS  is utilised to obtain static pull-in instability parameters of referential prismatic and variable-width  EANC s. Pull-in instability parameters of variable-width  EANC s, for various values of width variation parameters and the initial gap between electrodes, have been obtained. The aforementioned results have been validated with corresponding results obtained by three-dimensional finite element simulations performed using COMSOL Multiphysics ® . Compared to the referential prismatic  EANC , a significant augmentation in the pull-in displacement of the variable-width  EANC  has been obtained.

international journal for computational methods in engineering science and mechanics

Augmentation of the stable static travel range of electrostatically actuated slender nano-cantilevers by accounting for the influence of the van der Waals force