Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators

Abstract

This paper investigates the effect of dispersion (van der Waals and Casimir) forces on the pull-in instability of cantilever nano-actuators by considering their range of application. Adomian decomposition is introduced to obtain an analytical solution of the distributed parameter model. Dispersion forces decrease the pull-in deflection and voltage of a nano-actuator. However, the fringing field increases the pull-in deflection while decreasing the pull-in voltage of the actuator. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to van der Waals and Casimir attractions were determined. Furthermore, the proposed approach is capable of determining the stress distribution of the actuator at the onset of instability. It is seen that Casimir and van der Waals attractions effectively reduce the maximum value of stress resultants at the onset of instability. The results indicate that Adomian decomposition is a reliable method for simulating nano-structures at submicrometer ranges.

A new approach using hybrid power series – cuckoo search optimization algorithm to solve electrostatic pull-in instability and deflection of nano cantilever switches subject to van der waals attractions

“…In this case, the results of present study are compared with the numerical results as well as the results of Adomian decomposition method [3]. The numerical results are obtained using the dsolve function of MAPLE 14.0 mathematical software [21], [22].…”

“…1. The cross section of the beam is rectangular with thickness of h and width w. Length of the beam is denoted by L. The initial gap space between the cantilever beam and substrate plane is denoted by g. Considering the van der Waals attractions, electro static forces and fringling effects, the governing equation for the distributed model of the beam is written as [3]:…”

“…Many of the micro and nano devises including, switches in some microchips, pressure sensors, chemical sensors, values and pumps, are constructed using suspended beams and plates [1][2][3]. A cantilever nano switch is a beam suspended over a substrate.…”

“…They obtained analytical relations for pull-in instability of the actuators. Soroush et al [3] utilized a distributed parameter model to examine the pull-in instability and deflection of nano actuators. They [3] utilized the Adomian decomposition method to obtain a solution for deflection and pull-in instability of nano actuators.…”

“…Soroush et al [3] utilized a distributed parameter model to examine the pull-in instability and deflection of nano actuators. They [3] utilized the Adomian decomposition method to obtain a solution for deflection and pull-in instability of nano actuators. The results show that the Adomian series are capable to obtain a solution for pull-in instability of the nano actuators; however, the accuracy of the results is not good.…”