Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Casimir effect on the pull-in parameters of nanometer switches. Microsys Technol

Reduced-order models for microelectromechanical rectangular and circular plates incorporating the casimir force

In this paper, the static pull-in instability of beam-type nano-electromechanical systems (NEMS) is theoretically investigated considering the effect of Casimir attraction, elastic boundary conditions (BC) and size dependency. Rotational springs are utilized at each of the supported ends of the simply and doubly supported beams to model an elastic BC. The modified couple stress theory is applied to examine the size effects on the instability of nanostructures. In order to solve the nonlinear constitutive equation of nano-beams, modified Adomian decomposition (MAD) as well as the numerical method is employed. The results reveal significant influences of Casimir attraction, elastic BC and size dependency on the pull-in characteristics of NEMS. The obtained MAD solution agrees well with the numerical one.

http://ceramics-tabrizu.persiangig.com/document/1-s2.0-S1386947710006648-main.pdf

Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS

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.

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

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically, we reduce the governing two-dimensional nonlineartransient boundary-value problem to a single nonlinear ordinary differential equation. For thestatic problem, the pull-in voltage and the pull-in displacement are determined by solving apair of nonlinear algebraic equations. The fundamental vibration frequency corresponding toa deflected configuration of the microplate is determined by solving a linear algebraic equa-tion. The proposed reduced-order model allows for accurately estimating the combined effectsof van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflectionprofile with an extremely limited computational effort.

/pdf/effects-of-van-der-waals-force-and-thermal-stresses-on-pull-126aob01e3.pdf

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type mi cro and nano-switches. It is found that the error o f the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minim al when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam’s deflection, these two models not o nly are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to tha t the boundary conditions are not completely satisf ied when computing the numerical integration of the def lection.

Pull-in Instability of Micro-switch Actuators: Model Review

The influence of damping on the dynamical behavior of the electrostatic parallel-plate and torsional actuators with the van der Waals (vdW) or Casimir force (torque) is presented. The values of the pull-in parameters and the number of the equilibrium points do not change whether there is damping or not. The ability of equilibrium points is varied with the appearance of damping. One equilibrium point is an unstable saddle with a different damping coefficient, the other equilibrium point is a stable node when the damping coefficient is greater than some critical value, and otherwise it is a stable focus. Then there are two heteroclinic orbits passing from the unstable saddle point to the stable node or focus.

/pdf/influence-of-damping-on-the-dynamical-behavior-of-the-ci318bsrpg.pdf

Wen-Hui Lin

Papers

Pull-in Instability of Micro-switch Actuators: Model Review

Influence of Damping on the Dynamical Behavior of the Electrostatic Parallel-plate and Torsional Actuators with Intermolecular Forces