Investigation of the surface roughness effect on the nonlinear size-dependent pull-in instability of the beam-type nano-actuator

In this paper, the effect of surface roughness on the pull-in behavior of beam-type nano-actuator in the presence of intermolecular Van der Waals force has been investigated. In order to model the surface roughness, the roughness has been modeled as a step on the fixed electrode. Based on the modified couple stress theory and by using Hamilton’s principle, the governing equation and boundary conditions have been derived for the Euler–Bernoulli beam model. The differential quadrature method has been used to solve the nonlinear governing equations of the system. The results showed that the presence of roughness on the fixed electrode leads to an increase in the displacement of the beam and a reduction in the pull-in voltage, especially when the roughness is at the end of the beam and has considerable height. In this case, the freestanding behavior of the nano-actuator and the effect of roughness on the critical intermolecular force in the absence of electrostatic force are also evaluated. The results revealed a decrease in the critical intermolecular force due to the presence of roughness. However, increasing the material length scale parameters leads to an increase in the pull-in voltage and the freestanding values. Also, the size effect parameter decreases the displacement at the end of the beam.