A variational size-dependent model for electrostatically actuated NEMS incorporating nonlinearities and Casimir force

•A variational size-dependent model for the electrostatically actuated NEMS is presented.•The model incorporates nonlinearities and Casimir force.•The results reveal that Casimir force can reduce the external applied voltage.•Pull-in instability may occur without applied voltage due to Casimir force.•Size effect and Casimir force should be considered for precisely modeling NEMS.

A size-dependent model for the electrostatically actuated Nano-Electro-Mechanical Systems (NEMS) incorporating nonlinearities and Casimir force is presented by using a variational method. The governing equation and boundary conditions are derived with the help of strain gradient elasticity theory and Hamilton principle. Generalized differential quadrature (GDQ) method is employed to solve the problem numerically. The pull-in instability with Casimir force included is then studied. The results reveal that Casimir force, which is a spontaneous force between the two electrodes, can reduce the external applied voltage. With Casimir force incorporated, the pull-in instability occurs without voltage applied when the beam size is in nanoscale. The minimum gap and detachment length can be calculated from the present model for different beam size, which is important for NEMS design. Finally, discussions of size effect induced by the strain gradient terms reveal that the present model is more accurate since size effect play an important role when beam in nanoscale.