Closed Form Solutions for the Problem of Statical Behavior of Nano/Micromirrors Under the Effect of Capillary Force and Van Der Waals Force

2011 ◽  
Author(s):  
Ali Darvishian ◽  
Hamid Moeenfard ◽  
Hasan Zohoor ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Capillary Force ◽  
Rotation Angle ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Combined Effect ◽  
Geometrical Parameters ◽  
Closed Form Solutions ◽  
The Stability ◽  
Vdw Force ◽  
Stability Limits

The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW toque applied to the mirror. Finally analytical tool Homotopy Perturbation Mehtod (HPM) is utilized for prediction of the nano/micromirror behaviour under combined capillary and vdW force. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system.

INFLUENCE OF VAN DER WAALS FORCE ON STATIC BEHAVIOR OF NANO/MICROMIRRORS UNDER CAPILLARY FORCE

2012 ◽  
Vol 26 (07) ◽  
pp. 1250056 ◽  
Author(s):  
HAMID MOEENFARD ◽  
ALI DARVISHIAN ◽  
HASSAN ZOHOOR ◽  
MOHAMMAD TAGHI AHMADIAN
Keyword(s):  
Capillary Force ◽  
Rotation Angle ◽  
Van Der Waals ◽  
Geometrical Parameters ◽  
Static Behavior ◽  
Release Process ◽  
Dimensionless Equation ◽  
The Stability ◽  
Vdw Force ◽  
Stability Limits

In the current paper, the effect of van der Waals (vdW) force on the static behavior and pull-in characteristics of nano/micromirrors under capillary force is investigated. At first, the dimensionless equation governing the static behavior of nano/micromirrors is obtained. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that the existence of vdW force can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW force applied to the mirror. Finally, analytical tool Homotopy Perturbation Method (HPM) is utilized for prediction of the nano/micromirror behavior under combined capillary and vdW force. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. The results of this paper can be used for successful fabrication of nano/micromirrors using wet etching release process where capillary force plays a major role in the system.

Analytical Solutions for the Static Instability of Micro/Nano Mirrors Under the Combined Effect of Capillary Force and Casimir Force

2011 ◽  
Author(s):  
Hamid Moeenfard ◽  
Ali Darvishian ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Capillary Force ◽  
Casimir Force ◽  
Rotation Angle ◽  
Combined Effect ◽  
Geometrical Parameters ◽  
Casimir Forces ◽  
Tilting Angle ◽  
Static Instability ◽  
The Stability ◽  
Stability Limits

This paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and Casimir force. At the First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained. The dependency of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of casimir force can considerably reduce the stability limits of nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the casimir force applied to the mirror. Finally analytical tool Homotopy Perturbation Method (HPM) is utilized for prediction of the mirror’s behaviour under combined capillary and casimir forces. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system.

A Coupled Model Between Torsion and Bending in Nano/Micromirrors Under the Combined Effect of Van Der Waals Force and Capillary Force

2011 ◽  
Author(s):  
Hamid Moeenfard ◽  
Ali Darvishian ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Capillary Force ◽  
Coupling Effect ◽  
Van Der Waals ◽  
Coupled Model ◽  
Combined Effect ◽  
Static Behavior ◽  
Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Vdw Force

The coupling effect between torsion and bending in nano/micromirrors under the combined effect of capillary force and van der Waals (vdW) force is presented in this paper. At the first, the dimensionless equations governing the statical behavior of the nano/micromirror are obtained using the minimum total potential energy principle. Then the equations governing the pull-in state of the mirror are obtained using the implicit function theorem. The related results show that neglecting bending effect can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirror under combined vdW and capillary forces. It is observed that vdW force reduces the pull-in angle and pull-in deflection of the supporting torsion beams of the mirror. The static behavior of the nano/micromirror under capillary and vdW loading is also studied and the results reveal that the static behavior of the nano/micromirror under capillary and vdW forces highly depends on the bending of the torsion beams. The results of this paper can be used for a safe and stable design and fabrication of mirrors using the wet etching process, where the gap between the mirror and the underneath substrate is sufficiently small and as a results both capillary and vdW forces have significant role in the stability of the system.

scholarly journals Stability of a bi-layer free film: simultaneous or individual rupture events?

2015 ◽  
Vol 777 ◽  
pp. 27-49 ◽  
Author(s):  
Peter S. Stewart ◽  
Jie Feng ◽  
Laura S. Kimpton ◽  
Ian M. Griffiths ◽  
Howard A. Stone
Keyword(s):  
Van Der Waals ◽  
Liquid Interface ◽  
Van Der Waals Force ◽  
Interfacial Instability ◽  
Free Film ◽  
The Stability

We consider the stability of a long free film of liquid composed of two immiscible layers of differing viscosities, where each layer experiences a van der Waals force between its interfaces. We analyse the different ways in which the system can exhibit interfacial instability when the liquid layers are sufficiently thin. For an excess of surfactant on one gas–liquid interface, the coupling between the layers is relatively weak and the instability is manifested as temporally separated rupture events in each layer. Conversely, in the absence of surfactant, the coupling between the layers is much stronger and the instability is manifested as rupture of both layers simultaneously. These features are consistent with recent experimental observations.

The Effect of Porosity on Elastic Stability of Toroidal Shell Segments Made of Saturated Porous Functionally Graded Materials

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hadi Babaei ◽  
Mohsen Jabbari ◽  
M. Reza Eslami
Keyword(s):  
Elastic Stability ◽  
Functionally Graded ◽  
Toroidal Shell ◽  
Geometrical Parameters ◽  
Equilibrium Equations ◽  
Closed Form Solutions ◽  
Porous Shell ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability

Abstract This research deals with the stability analysis of shallow segments of the toroidal shell made of saturated porous functionally graded (FG) material. The nonhomogeneous material properties of porous shell are assumed to be functionally graded as a function of the thickness and porosity parameters. The porous toroidal shell segments with positive and negative Gaussian curvatures and nonuniform distributed porosity are considered. The nonlinear equilibrium equations of the porous shell are derived via the total potential energy of the system. The governing equations are obtained on the basis of classical thin shell theory and the assumptions of Biot's poroelasticity theory. The equations are a set of the coupled partial differential equations. The analytical method including the Airy stress function is used to solve the stability equations of porous shell under mechanical loads in three cases. Porous toroidal shell segments subjected to lateral pressure, axial compression, and hydrostatic pressure loads are analytically analyzed. Closed-form solutions are expressed for the elastic buckling behavior of the convex and concave porous toroidal shell segments. The effects of porosity distribution and geometrical parameters of the shell on the critical buckling loads of porous toroidal shell segments are studied.

MODELING THE INFLUENCE OF SURFACE EFFECT ON INSTABILITY OF NANO-CANTILEVER IN PRESENCE OF VAN DER WAALS FORCE

2013 ◽  
Vol 13 (04) ◽  
pp. 1250072 ◽  
Author(s):  
ALI KOOCHI ◽  
HOSSEIN HOSSEINI-TOUDESHKY ◽  
HAMID REZA OVESY ◽  
MOHAMADREZA ABADYAN
Keyword(s):  
Surface Energy ◽  
Numerical Solution ◽  
Surface Effect ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Adomian Decomposition ◽  
Vdw Force ◽  
Good Agreement

Surface effect often plays a significant role in the pull-in performance of nano-electromechanical systems (NEMS) but limited works have been conducted for taking this effect into account. Herein, the influence of surface effect has been investigated on instability behavior of cantilever nano-actuator in the presence of van der Waals force (vdW). Three different methods, i.e. an analytical modified Adomian decomposition (MAD), Lumped parameter model (LPM) and numerical solution have been applied to solve the governing equation of the system. The results demonstrate that surface effect reduces the pull-in voltage of the system. Moreover, surface energy causes the cantilever nano-actuator with the assigned parameter to deflect as a softer structure. It is found that while surface effect becomes important for low values of the cantilever nano-actuator thickness, vdW attraction is significant for low initial gap values. Surprisingly, the increase in the initial gap, enhances the contribution of surface effect in pull-in instability of the system while reduces the contribution of vdW attraction. Furthermore, the minimum initial gap and the detachment length of the cantilever nano-actuator that does not stick to the substrate due to vdW force and surface effect has been approximated. A good agreement has been observed between the values of instability parameters predicted via these three methods. Whilst compared to the instability voltage predicted by numerical solution, the pull-in voltage obtained by MAD series and LPM method is overestimated and underestimated, respectively.

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